%!PS-Adobe-2.0 %%Title: tr14 %%Creator: PrintMonitor %%CreationDate: Monday, May 23, 1994 %%Pages: (atend) %%BoundingBox: ? ? ? ? %%PageBoundingBox: 28 30 566 811 %%For: cianca %%DocumentProcSets: "(AppleDict md)" 71 0 %% © Copyright Apple Computer, Inc. 1989-91 All Rights Reserved. %%EndComments %%BeginProcSet: "(AppleDict md)" 71 0 userdict/LW{save statusdict/product get(LaserWriter)anchorsearch exch pop{dup length 0 eq{pop 1}{( Plus)eq{2}{3}ifelse}ifelse}{0}ifelse exch restore}bind put userdict/downloadOK known not{userdict/downloadOK{systemdict dup/eexec known exch/cexec known and LW dup 1 ne exch 2 ne and and vmstatus exch sub exch pop 120000 gt and}bind put}if userdict/type42known known not{userdict/type42known systemdict/resourcestatus known{42/FontType resourcestatus{pop pop true}{false}ifelse }{false}ifelse put}if type42known not downloadOK and {userdict begin /*charpath /charpath load def/charpathflag false def/charpath{userdict/charpathflag true put userdict/*charpath get exec userdict/charpathflag false put}bind def end}if userdict/checkload known not{userdict/checkload{{pop exec} {save 3 dict begin/mystring 6050 string def exch/endstring exch def{currentfile mystring readline not{stop}if endstring eq{exit}if}loop end restore pop}ifelse}bind put}if userdict/LW+{LW 2 eq}bind put userdict/ok known not{userdict/ok{systemdict/statusdict known dup{LW 0 gt and}if}bind put}if systemdict/currentpacking known{currentpacking true setpacking}if /md 270 dict def md begin /av 71 def /T true def/F false def/mtx matrix def/s75 75 string def/sa8 8 string def/sb8 8 string def /sc8 8 string def/sd8 8 string def/s1 ( ) def/pxs 1 def/pys 1 def /ns false def 1 0 mtx defaultmatrix dtransform exch atan/pa exch def/nlw .24 def/ppr [-32 -29.52 762 582.48] def /pgr [0 0 0 0] def /pgs 1 def/por true def/xb 500 array def/so true def/tso true def/fillflag false def/pnm 1 def/fmv true def /sfl false def/ma 0 def/invertflag false def/dbinvertflag false def/xflip false def/yflip false def/noflips true def/scaleby96 false def/fNote true def/fBitStretch true def /4colors false def/fg (Rvd\001\001\000\000\177) def /bdf{bind def}bind def /xdf{exch def}bdf /xl{neg exch neg translate}bdf /fp{pnsh 0 ne pnsv 0 ne and}bdf /nop{}bdf/lnop[/nop load]cvx bdf /vrb[ {fp{fg 6 get 0 ne{gsave stroke grestore}{gsave 1 setlinewidth pnsh pnsv scale stroke grestore}ifelse}if newpath}bind /eofill load dup /newpath load 2 index dup {clip newpath}bind {}bind dup 2 copy ]def /sgd systemdict/setpagedevice known{{2 dict begin/PreRenderingEnhance exch def/Policies 1 dict dup/PreRenderingEnhance 1 put def currentdict end setpagedevice}}{{pop}}ifelse bdf /svsc systemdict/currentcolorscreen known{{currentcolorscreen/dkspf xdf/dkrot xdf/dkfreq xdf/dyspf xdf/dyrot xdf/dyfreq xdf/dmspf xdf/dmrot xdf/dmfreq xdf /dcspf xdf/dcrot xdf/dcfreq xdf}}{{currentscreen/spf xdf/rot xdf/freq xdf}}ifelse bdf /doop{vrb exch get exec}bdf /psu{/udf xdf/tso xdf /fNote xdf/fBitStretch xdf/scaleby96 xdf/yflip xdf/xflip xdf /invertflag xdf/dbinvertflag invertflag statusdict begin version cvr 47.0 ge product (LaserWriter) eq not and end invertflag and {not}if def xflip yflip or{/noflips false def}if /pgs xdf 2 index .72 mul exch div/pys xdf div .72 mul/pxs xdf ppr astore pop pgr astore pop/por xdf sn and/so xdf}bdf /tab{userdict /11x17 known{userdict begin /11x17 load exec end}{statusdict /setpage known{statusdict begin 792 1224 1 setpage end}{statusdict /setpageparams known{statusdict begin 792 1224 0 1 setpageparams end}if}ifelse}ifelse}bdf /a3Size{userdict /a3 known{userdict begin /a3 load exec end}{statusdict /setpageparams known{statusdict begin 842 1191 0 1 setpageparams end}if}ifelse}bdf /txpose{fNote{smalls}{bigs}ifelse pgs get exec pxs pys scale ppr aload pop por{noflips{pop exch neg exch translate pop 1 -1 scale}if xflip yflip and{pop exch neg exch translate 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg translate}if xflip yflip not and{pop exch neg exch translate pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 translate}if yflip xflip not and{ppr 1 get neg ppr 0 get neg translate}if} {noflips{translate pop pop 270 rotate 1 -1 scale}if xflip yflip and{translate pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg translate}if xflip yflip not and{translate pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 translate}if yflip xflip not and{translate pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 exch translate}if}ifelse statusdict begin/waittimeout where{pop waittimeout 300 lt{statusdict/waittimeout 300 put}if}if end scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy translate .96 dup scale neg exch neg exch translate}if}bdf /fr{4 copy pgr aload pop 3 -1 roll add 3 1 roll exch add 6 2 roll 3 -1 roll sub 3 1 roll exch sub 3 -1 roll exch div 3 1 roll div exch scale pop pop xl}bdf /obl{{0.212557 mul}{pop 0}ifelse}bdf /sfd{ps fg 5 -1 roll get mul 100 div 0 ps 5 -1 roll obl ps neg 0 0 6a astore makefont setfont}bdf /fnt{findfont sfd}bdf /bt{sa 3 1 roll 3 index and put}bdf /sa(\000\000\000\000\000\000\000\000\000\000)def /fs{0 1 bt 1 2 bt 2 4 bt 3 8 bt 4 16 bt 5 32 bt 6 64 bt 7 128 bt sa exch 8 exch put}bdf /mx1 matrix def /mx2 matrix def /mx3 matrix def /bu{currentpoint 4colors{currentcmykcolor}{currentrgbcolor}ifelse currentlinewidth currentlinecap currentlinejoin currentdash exch aload length fg 5 sfl{1}{0}ifelse put pnsv pnsh 2t aload pop 3a aload pop mx2 aload pop mx1 aload pop mtx currentmatrix aload pop mx3 aload pop ps pm restore/ps xdf mx3 astore pop}bdf /bn{/pm save def mx3 setmatrix newpath 0 0 moveto ct dup 39 get 0 exch getinterval cvx exec mtx astore setmatrix mx1 astore pop mx2 astore pop 3a astore pop 2t astore pop/pnsh xdf/pnsv xdf gw /sfl fg 5 get 0 ne def array astore exch setdash setlinejoin setlinecap setlinewidth 4colors{mysetcmykcolor}{setrgbcolor}ifelse moveto}bdf /fc{save vmstatus exch sub 50000 lt {(%%[|0|]%%)=print flush}if pop restore}bdf /tc{32768 div add 3 1 roll 32768 div add 2t astore pop}bdf /3a [0 0 0] def /2t 2 array def /tp{3a astore pop}bdf /tt{mx2 currentmatrix pop currentpoint 2 copy 2t aload pop qa 2 copy translate 3a aload pop exch dup 0 eq {pop}{1 eq{-1 1}{1 -1}ifelse scale}ifelse rotate pop neg exch neg exch translate moveto}bdf /te{mx2 setmatrix}bdf /th{3 -1 roll div 3 1 roll exch div 2 copy mx1 scale pop scale/sfl true def}bdf /tu{1 1 mx1 itransform scale/sfl false def}bdf /ts{1 1 mx1 transform scale/sfl true def}bdf /fz{/ps xdf}bdf /dv{dup 0 ne{div}{pop}ifelse}bdf /pop4{pop pop pop pop}bdf /it{sfl{mx1 itransform}if}bdf /gm{exch it moveto}bdf/rm{it rmoveto}bdf /lm{currentpoint sfl{mx1 transform}if exch pop sub 0 exch it rmoveto}bdf /fm{statusdict/manualfeed known}bdf /se{statusdict exch/manualfeed exch put}bdf /mf{dup/ma exch def 0 gt{fm se/t1 5 st ok ma 1 gt and{/t2 0 st/t3 0 st statusdict/manualfeedtimeout 3600 put }if}if}bdf /jn{/statusdict where exch pop{statusdict exch /jobname exch put}if}bdf /pen{pnm mul/pnsh xdf pnm mul/pnsv xdf pnsh setlinewidth}bdf /min{2 copy gt{exch}if pop}bdf /max{2 copy lt{exch}if pop}bdf /dh{fg 6 1 put array astore dup {1 pxs div mul exch}forall astore exch pop exch pop exch setdash}bdf /ih[currentdash]def /rh{fg 6 0 put ih aload pop setdash}bdf /dl{gsave nlw pys div setlinewidth 0 setgray}bdf /dlin{exch currentpoint currentlinewidth 2 div dup translate newpath moveto lineto currentpoint stroke grestore moveto}bdf /lin{fg 6 get 0 ne{exch lineto currentpoint 0 doop moveto} {exch currentpoint/pnlv xdf/pnlh xdf gsave newpath/@1 xdf/@2 xdf fp{pnlh @2 lt{pnlv @1 ge {pnlh pnlv moveto @2 @1 lineto pnsh 0 rlineto 0 pnsv rlineto pnlh pnsh add pnlv pnsv add lineto pnsh neg 0 rlineto} {pnlh pnlv moveto pnsh 0 rlineto @2 pnsh add @1 lineto 0 pnsv rlineto pnsh neg 0 rlineto pnlh pnlv pnsv add lineto}ifelse}{pnlv @1 gt {@2 @1 moveto pnsh 0 rlineto pnlh pnsh add pnlv lineto 0 pnsv rlineto pnsh neg 0 rlineto @2 @1 pnsv add lineto}{pnlh pnlv moveto pnsh 0 rlineto 0 pnsv rlineto @2 pnsh add @1 pnsv add lineto pnsh neg 0 rlineto 0 pnsv neg rlineto}ifelse}ifelse closepath fill}if @2 @1 grestore moveto}ifelse}bdf /gw{/pnm fg 3 get fg 4 get div def}bdf /lw{fg exch 4 exch put fg exch 3 exch put gw pnsv pnsh pen}bdf /barc{/@1 xdf/@2 xdf/@3 xdf/@4 xdf/@5 xdf /@6 xdf/@7 xdf/@8 xdf gsave @5 @7 add 2 div @6 @8 add 2 div translate newpath 0 0 moveto @5 @7 sub @6 @8 sub mtx currentmatrix pop scale @1{newpath}if 0 0 0.5 @4 @3 arc @4 @3 sub abs 360 ge{closepath}if mtx setmatrix @2 doop grestore}bdf /ar{dup 0 eq barc}bdf /ov{0 exch 360 exch true barc}bdf /rc{dup/@t xdf 0 eq{4 copy 3 -1 roll eq 3 1 roll eq and{pnsv 2 div sub exch pnsh 2 div sub exch 4 2 roll pnsv 2 div add exch pnsh 2 div add exch /@t 1 def}if}if currentpoint 6 2 roll newpath 4 copy 4 2 roll exch moveto 6 -1 roll lineto lineto lineto closepath @t doop moveto}bdf /mup{dup pnsh 2 div le exch pnsv 2 div le or}bdf /rr{/@1 xdf 2. div/@2 xdf 2. div/@3 xdf /@4 xdf/@5 xdf/@6 xdf/@7 xdf @7 @5 eq @6 @4 eq @2 mup or or{@7 @6 @5 @4 @1 rc} {@4 @6 sub 2. div dup @2 lt{/@2 xdf}{pop}ifelse @5 @7 sub 2. div dup @2 lt{/@2 xdf}{pop}ifelse @1 0 eq{/@2 @2 pnsh 2 div 2 copy gt{sub def}{0 pop4}ifelse}if currentpoint newpath @4 @6 add 2. div @7 moveto @4 @7 @4 @5 @2 arcto pop4 @4 @5 @6 @5 @2 arcto pop4 @6 @5 @6 @7 @2 arcto pop4 @6 @7 @4 @7 @2 arcto pop4 closepath @1 doop moveto}ifelse}bdf /pr{gsave newpath/pl{exch moveto/pl{exch lineto}def}def}bdf /pl{exch lineto}bdf /ep{dup 0 eq{{moveto}{exch lin}{}{(%%[|1|]%%)= flush}pathforall pop grestore}{doop grestore}ifelse currentpoint newpath moveto}bdf /gr{64. div setgray}bdf /savescreen{ns not{/ns true def systemdict/currentcolorscreen known{currentcolorscreen/pkspf xdf/pkrot xdf/pkfreq xdf/pyspf xdf/pyrot xdf/pyfreq xdf/pmspf xdf/pmrot xdf/pmfreq xdf /pcspf xdf/pcrot xdf/pcfreq xdf}{currentscreen/sspf xdf/srot xdf/sfreq xdf}ifelse}if}bdf /restorescreen{/ns false def systemdict/setcolorscreen known{pcfreq pcrot/pcspf load pmfreq pmrot/pmspf load pyfreq pyrot/pyspf load pkfreq pkrot/pkspf load setcolorscreen}{sfreq srot/sspf load setscreen}ifelse}bdf /pat{savescreen sa8 copy pop 9.375 pa por not{90 add}if{1 add 4 mul cvi sa8 exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and}setscreen exch not{gr}{pop}ifelse}bdf /sg{restorescreen gr}bdf /cpat{savescreen 10 2 roll 7 -1 roll sa8 copy pop 9.375 pa por not{90 add}if{1 add 4 mul cvi sa8 exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and}8 -1 roll sb8 copy pop 9.375 pa por not{90 add}if{1 add 4 mul cvi sb8 exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and}9 -1 roll sc8 copy pop 9.375 pa por not{90 add}if{1 add 4 mul cvi sc8 exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and}10 -1 roll sd8 copy pop 9.375 pa por not{90 add}if{1 add 4 mul cvi sd8 exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and}psuedo1 dsc 4{4 -1 roll 1 exch 64 div sub}repeat mysetcmykcolor pop pop}bdf systemdict/setcolorscreen known{/psuedo1 lnop bdf/dsc/setcolorscreen load def}{/psuedo1{16{pop}repeat sa8 copy pop 9.375 pa por not{90 add}if{1 add 4 mul cvi sa8 exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and}}bdf /bwsc{setscreen dup gr 0 exch 0 exch 64 exch 64 exch 64 exch}bdf/dsc/bwsc load def }ifelse systemdict/setcmykcolor known{/mysetcmykcolor /setcmykcolor load def}{/mysetcmykcolor{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll}repeat setrgbcolor pop}bdf}ifelse /dc{transform round .5 sub exch round .5 sub exch itransform}bdf /sn{userdict/smooth4 known}bdf /x8{3 bitshift}bdf /x4{2 bitshift}bdf /d4{-2 bitshift}bdf /d8{-3 bitshift}bdf /rb{15 add -4 bitshift 1 bitshift}bdf /db{/@7 save def/@1 xdf/@2 xdf/@3 xdf/@4 xdf/@5 xdf/@6 @5 @3 4 add mul def dc translate scale/xdbit 1 1 idtransform abs/ydbit exch def abs def{0 0 1 ydbit add 1 10 rc clip}if @1 0 eq @1 4 eq or{currentrgbcolor 1 setgray ydbit 0 1 ydbit add 1 2 rc setrgbcolor}if @1 3 eq @1 7 eq or{1 setgray}{currentrgbcolor 2 index eq exch 2 index eq and exch pop{0 setgray}if}ifelse/@9 @1 0 eq @1 1 eq @1 3 eq or or dbinvertflag xor def/@13 @6 def @2 fBitStretch or{/@10 @4 x4 def/@11 @3 x4 def/@12 @10 rb def/@13 @12 @11 mul def/@15 1 1 dtransform abs/calcY 1 index def round cvi/@14 exch def abs/calcX 1 index def round cvi scaleby96 not{1 add}if def/@16 @15 rb def/@17 @16 @14 mul def}if sn @13 60000 lt and @2 fBitStretch or and{mtx currentmatrix dup 1 get exch 2 get 0. eq exch 0. eq and @17 60000 lt and fBitStretch and{@16 3 bitshift @14 @9 [calcX 0 0 calcY 0 0]{@17 string @13 string currentfile @6 string readhexstring pop 1 index @4 @3 @5 @12 @2 smooth4 @10 @11 @12 dup string 5 index @15 @14 @16 dup string stretch}imagemask}{@12 x8 @11 @9 [@10 0 0 @11 0 0]{@13 string currentfile @6 string readhexstring pop 1 index @4 @3 @5 @12 @2 smooth4}imagemask}ifelse}{@5 3 bitshift @3 4 add @9 [@4 0 0 @3 0 2]{currentfile @6 string readhexstring pop}imagemask}ifelse @7 restore}bdf systemdict/setcmykcolor known{/psuedo lnop bdf/di/colorimage load def}{/routines[{.3 mul add 1}bind{.59 mul add 2}bind{.11 mul add round cvi str exch i exch put/i i 1 add def 0 0}bind]def /psuedo{/i 0 def 0 exch 0 exch{exch routines exch get exec}forall pop pop str}bdf/bwi{pop pop image}bdf/di/bwi load def}ifelse /cdb{/@7 save def/@1 xdf/@2 xdf/@3 xdf/@4 xdf/@5 xdf systemdict/setcmykcolor known not{dc}if translate scale /@6 xdf /@18 @5 dup 60000 ge{pop 60000}if string def @6 not{/str @18 0 @18 length 3 idiv getinterval def}if @4 @3 8 [@4 0 0 @3 0 0]@6{{currentfile @18 readhexstring pop}image}{{currentfile @18 readhexstring pop psuedo}false 3 di}ifelse @7 restore}bdf /wd 16 dict def /mfont 14 dict def /mdf{mfont wcheck not{/mfont 14 dict def}if mfont begin xdf end}bdf /cf{{1 index/FID ne{def}{pop pop}ifelse}forall}bdf/rf{/@1 exch def/@2 exch def FontDirectory @2 known{cleartomark pop}{findfont dup begin dup length @1 add dict begin cf{/Encoding macvec def}{Encoding dup length array copy/Encoding exch def counttomark 2 idiv{Encoding 3 1 roll put}repeat}ifelse pop exec currentdict end end @2 exch definefont pop}ifelse}bdf /bmbc{exch begin wd begin /cr xdf save CharTable cr 6 mul 6 getinterval{}forall /bitheight xdf/bitwidth xdf .96 div/width xdf Gkernmax add/XOffset xdf Gdescent add/YOffset xdf/rowbytes xdf rowbytes 255 eq{0 0 0 0 0 0 setcachedevice} {Gnormsize dup scale width 0 XOffset YOffset bitwidth XOffset add bitheight YOffset add setcachedevice rowbytes 0 ne{ XOffset YOffset translate newpath 0 0 moveto bitwidth bitheight scale sn{ /xSmt bitwidth x4 def /ySmt bitheight x4 def /rSmt xSmt rb def rSmt x8 ySmt true [xSmt 0 0 ySmt neg 0 ySmt] {rSmt ySmt mul string CharData cr get 1 index bitwidth bitheight rowbytes rSmt tso smooth4} }{rowbytes 3 bitshift bitheight 4 add true [bitwidth 0 0 bitheight neg 0 bitheight 2 add] {CharData cr get} }ifelse imagemask }if }ifelse restore end end }bdf /bb{.96 exch div/Gnormsize mdf 2 index /Gkernmax mdf 1 index/Gdescent mdf 3 index div 4 1 roll 2 index div 1. 5 2 roll exch div 4 1 roll 4 array astore/FontBBox mdf }bdf /cdf{mfont/CharData get 3 1 roll put}bdf /bf{ mfont begin /FontType 3 def /FontMatrix [1 0 0 1 0 0] def /Encoding macvec def /MFontType 0 def /BuildChar/bmbc load def end mfont definefont pop }bdf /wi LW 1 eq{{gsave 0 0 0 0 0 0 0 0 moveto lineto lineto lineto closepath clip stringwidth grestore}bind}{/stringwidth load}ifelse def /aps{0 get 124 eq}bdf /xc{s75 cvs dup}bdf /xp{put cvn}bdf /scs{xc 3 67 put dup 0 95 xp}bdf /sos{xc 3 79 xp}bdf /sbs{xc 1 66 xp}bdf /sis{xc 2 73 xp}bdf /sob{xc 2 79 xp}bdf /sss{xc 4 83 xp}bdf /dd{exch 1 index add 3 1 roll add exch}bdf /smc{moveto dup show}bdf /ndf2{udf{dup /FontType get 0 eq{/FDepVector get{dup /FontType get 0 eq{ndf2}{dup /df2 known{begin df2 0 null put end }{pop}ifelse}ifelse}forall}{/df2 known{dup begin df2 0 null put end}if}ifelse}{pop}ifelse}bdf /kwn{FontDirectory 1 index known{findfont dup ndf2 exch pop}}bdf /gl{1 currentgray sub setgray}bdf /newmm{dup /FontType get 0 eq{dup maxlength dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall currentdict end dup /FDepVector 2 copy get[exch 6 index exch 6 index exch{newmm 3 1 roll}forall pop pop] put dup }{/mfont 10 dict def mfont begin/FontMatrix [1 0 0 1 0 0] def /FontType 3 def/Encoding macvec def/df 1 index def/df2 1 array def/FontBBox [0 0 1 1] def/StyleCode 2 index def /mbc{bcarray StyleCode get}def/BuildChar{exch begin wd begin/cr exch def/cs s1 dup 0 cr put def df /MFontType known not{ df2 0 get null eq{df dup length 2 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall /StrokeWidth 1 0 FontMatrix idtransform pop dup nlw mul pys div ps div exch 0.012 mul 2 copy le{exch}if pop def/PaintType 2 def currentdict end /q exch definefont df2 exch 0 exch put}if}if mbc exec end end}def end mfont}ifelse 3 index exch definefont exch pop}bdf /mb{dup sbs kwn{0 2 index findfont newmm exch pop exch pop exch pop}ifelse sfd}bdf /mo{dup sos kwn{2 2 index findfont newmm exch pop exch pop exch pop}ifelse sfd}bdf /ms{dup sss kwn{4 2 index findfont newmm exch pop exch pop exch pop}ifelse sfd}bdf /ou{dup sos kwn{mfont/df2 known{mfont begin df2 0 null put end}if 3 2 index findfont newmm exch pop exch pop exch pop}ifelse sfd}bdf /su{dup sss kwn{mfont/df2 known{mfont begin df2 0 null put end}if 5 2 index findfont newmm exch pop exch pop exch pop}ifelse sfd}bdf /ao{/fmv true def ou}bdf/as{/fmv true def su}bdf /vo{/fmv false def ou}bdf/vs{/fmv false def su}bdf /c{currentrgbcolor dup 4 1 roll eq 3 1 roll eq and/gray xdf}bdf /bcarray[{/da .03 def df setfont gsave cs wi 1 index 0 ne{exch da add exch}if grestore setcharwidth cs 0 0 smc da 0 smc da da smc 0 da moveto show}bind dup{/da 1 ps div def df setfont gsave cs wi 1 index 0 ne{exch da add exch}if grestore setcharwidth cs 0 0 smc da 0 smc da da smc 0 da smc c gray{gl}{1 setgray}ifelse da 2. div dup moveto show}bind {df setfont gsave cs wi grestore setcharwidth c gray{gl}{currentrgbcolor 1 setgray}ifelse cs 0 0 smc df2 0 get setfont gray{gl}{4 1 roll setrgbcolor}ifelse 0 0 moveto show}bind {/da 1 ps div def/ds .05 def/da2 da 2. div def df setfont gsave cs wi 1 index 0 ne{exch ds add da2 add exch}if grestore setcharwidth cs ds da2 add .01 add 0 smc 0 ds da2 sub translate 0 0 smc da 0 smc da da smc 0 da smc c gray{gl}{1 setgray}ifelse da 2. div dup moveto show}bind {/da .05 def df setfont gsave cs wi 1 index 0 ne{exch da add exch}if grestore setcharwidth c cs da .01 add 0 smc 0 da translate gray{gl}{currentrgbcolor 1 setgray 4 -1 roll}ifelse 0 0 smc gray{gl}{4 1 roll setrgbcolor}ifelse df2 0 get setfont 0 0 moveto show}bind]def /st{1000 mul usertime add dup 2147483647 gt{2147483647 sub}if def}bdf /the{usertime sub dup 0 lt exch -2147483648 gt and}bdf /6a 6 array def /2a 2 array def /3q 3 array def /qs{3 -1 roll sub exch 3 -1 roll sub exch}bdf /qa{3 -1 roll add exch 3 -1 roll add exch}bdf /qm{3 -1 roll 1 index mul 3 1 roll mul}bdf /qn{6a exch get mul}bdf /qA .166667 def/qB .833333 def/qC .5 def /qx{6a astore pop qA 0 qn qB 2 qn add qA 1 qn qB 3 qn add qB 2 qn qA 4 qn add qB 3 qn qA 5 qn add qC 2 qn qC 4 qn add qC 3 qn qC 5 qn add}bdf /qp{6 copy 12 -2 roll pop pop}bdf /qc{exch qp qx curveto}bdf /qi{{exch 4 copy 2a astore aload pop qa .5 qm newpath moveto}{exch 2 copy 6 -2 roll 2 qm qs 4 2 roll}ifelse}bdf /qq{{qc 2a aload pop qx curveto}{exch 4 copy qs qa qx curveto}ifelse}bdf /pt{currentpoint newpath moveto}bdf /qf{/fillflag true def}bdf /ec{dup 4 and 0 ne{closepath}if 1 and 0 ne{0 doop}if grestore currentpoint newpath moveto/fillflag false def}bdf /eu{currentpoint fp{0 ep}{grestore newpath}ifelse moveto/fillflag false def}bdf /bp{currentpoint newpath 2 copy moveto}bdf /ef{gsave fillflag{gsave eofill grestore}if}bdf /sm{0 exch{@1 eq{1 add}if}forall}bdf /lshow{4 1 roll exch/@1 exch def{1 index wi pop sub 1 index sm dv 0 @1 4 -1 roll widthshow}{1 index wi pop sub 1 index dup sm 10 mul exch length 1 sub add dv dup 10. mul 0 @1 4 -1 roll 0 6 -1 roll awidthshow}ifelse}bdf /setTxMode{sa 9 2 index put exch not{3 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ffffffffffffffffffffffffff8000383ffc0f8027cce01e0201007fc1e0000fffffffff fffffffffffffffff0 ffffffffffffffffffffffffffe0000781ffcfc027cce01e0001bff81f00003fffffffff fffffffffffffffff0 fffffffffffffffffffffffffffc0000f01fffe003c0e01f0001ff80780001ffffffffff fffffffffffffffff0 ffffffffffffffffffffffffffff00000f00fff80380e01f0037f80780000fffffffffff fffffffffffffffff0 ffffffffffffffffffffffffffffe00000f00fffe7fff03fffff007800003fffffffffff fffffffffffffffff0 fffffffffffffffffffffffffffff800000f800fffffffffff000f800001ffffffffffff fffffffffffffffff0 ffffffffffffffffffffffffffffff000000fc0003ffffff8003f8000007ffffffffffff fffffffffffffffff0 ffffffffffffffffffffffffffffffe0000007f00000000003fe0000003fffffffffffff fffffffffffffffff0 fffffffffffffffffffffffffffffffc0000000ffe000003ff00000003ffffffffffffff fffffffffffffffff0 ffffffffffffffffffffffffffffffffc000000003ffffff000000001fffffffffffffff fffffffffffffffff0 fffffffffffffffffffffffffffffffffc0000000000000000000001ffffffffffffffff fffffffffffffffff0 ffffffffffffffffffffffffffffffffffe00000000000000000000fffffffffffffffff fffffffffffffffff0 fffffffffffffffffffffffffffffffffffe000000000000000003ffffffffffffffffff fffffffffffffffff0 fffffffffffffffffffffffffffffffffffff8000000000000007fffffffffffffffffff fffffffffffffffff0 ffffffffffffffffffffffffffffffffffffffc000000000000fffffffffffffffffffff fffffffffffffffff0 ffffffffffffffffffffffffffffffffffffffffc00000003fffffffffffffffffffffff fffffffffffffffff0 > imagemask grestore pse -30 -28 xl 196 69 gm (nc 0 0 781 538 6 rc)kp F 1 setTxMode 1 fs bu fc {}mark T /Times-Bold /|______Times-Bold 0 rf bn 18 fz bu fc 2 F /|______Times-Bold fnt bn (A Comparison of Parallel Search Algorithms based on)show 213 225 gm (Tree Splitting)show 289 227 gm 14 fz bu fc 2 F /|______Times-Bold fnt bn (Paolo Ciancarini)show 410 182 gm (Technical Report UBLCS-94-14)show 439 249 gm 0 fs bu fc {}mark T /Times-Roman /|______Times-Roman 0 rf bn bu fc 2 F /|______Times-Roman fnt bn (May 1994)show 633 183 gm (Laboratory for Computer Science)show 651 215 gm (University of Bologna)show 669 199 gm (Piazza di Porta S. Donato, 5)show 687 216 gm (40127 Bologna \(Italy\))show F T cp %%Page: ? 2 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 139 79 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Times-Roman fnt bn 1.17721 0. 32 0.11772 0.(The University of Bologna Laboratory for Computer Science Research Technical Reports are available via)awidthshow 153 79 gm 0.77774 0. 32 0.07777 0.(anonymous FTP from the area )awidthshow bu fc {}mark T /Courier /|______Courier 0 rf bn bu fc 2 F /|______Courier fnt bn 0.29316 0.(ftp.cs.unibo.it:/pub/TR/UBLCS)ashow bu fc 2 F /|______Times-Roman fnt bn 0.91796 0. 32 0.09179 0.( in compressed PostScript format.)awidthshow 167 79 gm 1.05239 0. 32 0.10523 0.(Abstracts are available from the same host in the directory )awidthshow bu fc 2 F /|______Courier fnt bn 0.42799 0.(/pub/TR/UBLCS/ABSTRACTS)ashow bu fc 2 F /|______Times-Roman fnt bn 0.83404 0. 32 0.08340 0.( in plain text)awidthshow 181 79 gm (format. All local authors can be reached via e-mail at the address )show 2 fs bu fc {}mark T /Times-Italic /|______Times-Italic 0 rf bn bu fc 2 F /|______Times-Italic fnt bn (last-name)show 0 fs bu fc 2 F /|______Courier fnt bn (@cs.unibo.it.)show 207 79 gm 1 fs 11 fz bu fc 2 F /|______Times-Bold fnt bn (UBLCS Technical Report Series)show 232 80 gm 0 fs 10 fz bu fc 2 F /|______Times-Roman fnt bn (93-1)show 232 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 2.19955 0. 32 0.21995 0.(Consistent Global States of Distributed Systems: Fundamental Concepts and Mechanism)awidthshow 0 fs bu fc 2 F /|______Times-Roman fnt bn 1.11801 0. 32 0.11180 0.(, by \205.)awidthshow 245 110 gm (Babao)show 245 136 gm (g;\371lu and K. Marzullo, January 1993.)show 258 80 gm (93-2)show 258 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (Understanding Non-Blocking Atomic Commitment)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by \205. Babao)show 258 368 gm (g;\371lu and S. Toueg, January 1993.)show 271 80 gm (93-3)show 271 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (Anchors and Paths in a Hypertext Publishing System)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by C. Maioli and F. Vitali, February 1993.)show 284 80 gm (93-4)show 284 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (A Formalization of Priority Inversion)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by \205. Babao)show 284 316 gm (g;\371lu, K. Marzullo and F. Schneider, March 1993.)show 297 80 gm (93-5)show 297 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.68313 0. 32 0.06831 0.(Some Modifications to the Dexter Model for the Formal Description of Hypertexts)awidthshow 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.52368 0. 32 0.05236 0.(, by S. Lamberti, C.)awidthshow 310 110 gm (Maioli and F. Vitali, April 1993.)show 323 80 gm (93-6)show 323 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.50613 0. 32 0.05061 0.(Versioning Issues in a Collaborative Distributed Hypertext)awidthshow 11 fz bu fc 2 F /|______Times-Italic fnt bn ( )show 323 354 gm 10 fz bu fc 2 F /|______Times-Italic fnt bn 0.18540 0.(System)ashow 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.49468 0. 32 0.04946 0.(, by C. Maioli, S. Sola and F. Vitali,)awidthshow 336 110 gm (April 1993.)show 349 80 gm (93-7)show 349 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (Distributed Programming with Logic Tuple Spaces)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by P. Ciancarini, April 1993.)show 362 80 gm (93-8)show 362 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (Coordinating Rule-Based Software Processes with ESP)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by P. Ciancarini, April 1993.)show 375 80 gm (93-9)show 375 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (What is Logic Programming good for in Software Engineering)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by P. Ciancarini and G. Levi, April 1993.)show 388 80 gm (93-10)show 388 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.84320 0. 32 0.08432 0.(Scheduling Real Time Tasks: A Performance Study)awidthshow 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.59097 0. 32 0.05909 0.(, by F. Panzieri, L. Donatiello and L. Poretti, May)awidthshow 401 110 gm (1993.)show 414 80 gm (93-11)show 414 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.58334 0. 32 0.05833 0.(Specification and Detection of Behavioral Patterns in Distributed Computations)awidthshow 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.37704 0. 32 0.03770 0.(, by \205. Babao)awidthshow 414 498 gm 0.54534 0. 32 0.05453 0.(g;\371lu and)awidthshow 427 110 gm (M. Raynal, May 1993.)show 440 80 gm (93-12)show 440 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (Interaction Systems II: The Practice of Optimal Reductions)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by A. Asperti and C. Laneve, May 1993.)show 453 80 gm (93-13)show 453 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 1.00616 0. 32 0.10061 0.(Reliability Analysis of Tree-Based Structures and its Application to Fault-Tolerant VLSI Systems)awidthshow 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.61645 0. 32 0.06164 0.(, by)awidthshow 466 110 gm (Marco Roccetti, June 1993.)show 479 80 gm (93-14)show 479 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (Guard Compilation in Logic Shared Dataspace Languages)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by M. Garpari, June 1993.)show 492 80 gm (93-15)show 492 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 1.16424 0. 32 0.11642 0.(Data Algorithm: A Numerical Method to Extract Shape Information from Gray Scale Images)awidthshow 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.66116 0. 32 0.06611 0.(, by R.)awidthshow 505 110 gm (Davoli and F. Tamburini, June 1993.)show 518 80 gm (93-16)show 518 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (Towards Performance Evaluation in Process Algebra)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by R. Gorrieri and M. Roccetti, July 1993.)show 531 80 gm (93-17)show 531 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (Split and ST Bisimulation Semantics)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by R. Gorrieri and C. Laneve, July 1993.)show 544 80 gm (93-18)show 544 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (Multilanguage Interoperability)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by G. Attardi and M. Gaspari, July 1993.)show 557 80 gm (93-19)show 557 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.20431 0. 32 0.02043 0.(HERMES: an Expert System for the Prognosis of Hepatic Diseases)awidthshow 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.14709 0. 32 0.01470 0.(, by I. Bonf\210, C. Maioli, F. Sarti, G.L.)awidthshow 570 110 gm (Milandri and P.R. Dal Monte, September 1993)show 583 80 gm (93-20)show 583 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (An Information Flow Security Property for CCS)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by R. Focardi and R. Gorrieri, October 1993.)show 596 80 gm (93-21)show 596 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (A Classification of Security Properties)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by R. Focardi and R. Gorrieri, October 1993.)show 609 80 gm (93-22)show 609 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (Real Time Systems: A Tutorial)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by F. Panzieri and R. Davoli, October 1993.)show 622 80 gm (93-23)show 622 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn -0.00643 0.(A Scalable Architecture for Reliable Distributed Multimedia Applications)ashow 0 fs bu fc 2 F /|______Times-Roman fnt bn -0.00637 0.(, by F. Panzieri and M. Roccetti,)ashow 635 110 gm (October 1993.)show 648 80 gm (93-24)show 648 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (Wide-Area Distribution Issues in Hypertext Systems)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by C. Maioli, S. Sola and F. Vitali, October 1993.)show 661 80 gm (93-25)show 661 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (On Relating Some Models for Concurrency)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (, by P. Degano, R. Gorrieri and S. Vigna, October 1993.)show 674 80 gm (93-26)show 674 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 1.45263 0. 32 0.14526 0.(Axiomatising ST Bisimulation Equivalence)awidthshow 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.88378 0. 32 0.08837 0.(, by N. Busi, R. van Glabbeek and R. Gorrieri, December)awidthshow 687 110 gm (1993.)show 700 80 gm (93-27)show 700 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 1.48498 0. 32 0.14849 0.(A Theory of Processes with Durational Actions)awidthshow 0 fs bu fc 2 F /|______Times-Roman fnt bn 1.30096 0. 32 0.13009 0.(, by R. Gorrieri, M. Roccetti and E. Stancampiano,)awidthshow 713 110 gm (December 1993.)show F T cp %%Page: ? 3 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 801 525 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn (1)show 146 79 gm 1 fs 18 fz bu fc 2 F /|______Times-Bold fnt bn 2.25738 0. 32 0.22573 0.(A Comparison of Parallel Search Algorithms based on)awidthshow 164 79 gm (Tree Splitting)show 217 79 gm 12 fz bu fc 2 F /|______Times-Bold fnt bn (Paolo Ciancarini)show 0 -4 rm 9 fz bu fc 2 F /|______Times-Bold fnt bn (1)show 294 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn (Technical Report UBLCS-94-14)show 322 79 gm (May 1994)show 363 79 gm 1 fs bu fc 2 F /|______Times-Bold fnt bn (Abstract)show 380 79 gm 2 fs 10 fz bu fc 2 F /|______Times-Italic fnt bn 0.01831 0. 32 0.00183 0.(We have used a distributed programming environment to compare a number of parallel search algorithms in the)awidthshow 394 79 gm 0.43136 0. 32 0.04313 0.(domain of chess. The environment runs on a network of workstations; it is based on Linda for coordination of)awidthshow 408 79 gm 0.84838 0. 32 0.08483 0.(the search and on GNUChess for chess knowledge. In order to make a practical comparison, we have built)awidthshow 422 79 gm 0.43441 0. 32 0.04344 0.(several parallel programs using different search algorithms. We have formalized and classified the concept of)awidthshow 436 79 gm 0.34042 0. 32 0.03404 0.(parallel search algorithms based game tree splitting. The algorithms have been classified in two main classes:)awidthshow 450 79 gm 0.46676 0. 32 0.04667 0.(static and dynamic. We show that on a workstation network static algorithms are more efficient than dynamic)awidthshow 464 79 gm (ones. Our results confirm and broaden older works by Marsland, Campbell, Schaeffer, and others.)show 739 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn (\321\321\321)show 749 79 gm 1 fs 9 fz bu fc 2 F /|______Times-Bold fnt bn (1)show 0 1 rm 0 fs bu fc 2 F /|______Times-Roman fnt bn (.)show 750 94 gm (E-mail: cianca@cs.unibo.it)show F T cp %%Page: ? 4 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 336 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs bu fc {}mark T /Helvetica /|______Helvetica 0 rf bn 10 fz bu fc 2 F /|______Helvetica fnt bn (A Comparison of Parallel Search Algorithms)show 773 79 gm (UBLCS-94-14)show 773 519 gm (2)show 134 79 gm 1 fs 12 fz bu fc 2 F /|______Times-Bold fnt bn (1. Introduction)show 147 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 1.81762 0. 32 0.18176 0.(The alphabeta algorithm is the basis of most sequential programs that search game trees. Its)awidthshow 158 79 gm 0.35644 0. 32 0.03564 0.(efficiency is decisive in chess playing programs, whose playing strength can be precisely measured)awidthshow 169 79 gm 1.08215 0. 32 0.10821 0.(using the Elo system [Elo86]. For instance, some experiments found that improving 5 times the)awidthshow 180 79 gm 0.24139 0. 32 0.02413 0.(running time of such an algorithm the playing strength of a chess programs improves about 200 Elo)awidthshow 191 79 gm 0.08392 0. 32 0.00839 0.(points [Tho82]. One could expect that multiprocessors and multicomputers should be very helpful in)awidthshow 202 79 gm 1.07360 0. 32 0.10736 0.(building stronger chess programs. However, it is well known that the efficient parallelization of)awidthshow 213 79 gm 0.75637 0. 32 0.07563 0.(alphabeta is a difficult problem [FinFis82]. Several different ways to parallelism in chess playing)awidthshow 224 79 gm (programs have been explored; a short survey is found in [BalVRe86]. The main methods are:)show 236 88 gm 2.15698 0. 32 0.21569 0.(i\) Parallel aspiration search [Bau78]: the alphabeta window is partitioned in a number of)awidthshow 247 101 gm 0.00518 0. 32 0.00051 0.(contiguous segments, that are used by different processors to explore the same game tree; this is)awidthshow 258 101 gm (a form of OR-parallelism.)show 271 88 gm 1.79580 0. 32 0.17958 0.(ii\) Parallel evaluation by special hardware; )awidthshow 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.39163 0.(e.g.)ashow 0 fs bu fc 2 F /|______Times-Roman fnt bn 1.88949 0. 32 0.18894 0.(, HITECH uses parallel hardware for move)awidthshow 282 101 gm 2.09396 0. 32 0.20939 0.(generation [Ebe86], while Deep Thought [Hsu90] uses parallel hardware for evaluating)awidthshow 293 101 gm (positions.)show 306 88 gm 0.44219 0. 32 0.04421 0.(iii\) Mapping the search space on the processor set by a hash function: this is advantageous if the)awidthshow 317 101 gm 1.15493 0. 32 0.11549 0.(search space contains several duplicate states; )awidthshow 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.24205 0.(e.g.)ashow 0 fs bu fc 2 F /|______Times-Roman fnt bn 1.09634 0. 32 0.10963 0.(, [Sti91] describes how the whole search)awidthshow 328 101 gm (space of some chess endings was mapped on a Connection Machine.)show 341 88 gm 0.93551 0. 32 0.09355 0.(iv\) Parallel search of \322splitted\323 game tree: the game tree is decomposed assigning its nodes to)awidthshow 352 101 gm (different search processes.)show 364 79 gm 0.66818 0. 32 0.06681 0.(The last method is the most widely studied and used. For instance, in [MarCam82] several search)awidthshow 375 79 gm 0.26077 0. 32 0.02607 0.(algorithms were described and compared; other experiments with different algorithms are described)awidthshow 386 79 gm 0.56335 0. 32 0.05633 0.(in [MOS86]. However, after those seminal papers we found no newer survey works on comparing)awidthshow 397 79 gm 0.09002 0. 32 0.00900 0.(parallel algorithms, although new ones have been invented. We decided to test the flexibility and the)awidthshow 408 79 gm 0.59478 0. 32 0.05947 0.(performance of a modern parallel language in implementing such algorithms on a general purpose)awidthshow 419 79 gm (network.)show 430 79 gm 2.87628 0. 32 0.28762 0.(Thus, in this paper we compare some parallel search algorithms based on tree splitting,)awidthshow 441 79 gm 1.16760 0. 32 0.11676 0.(implementing them all in the same hw/sw environment, )awidthshow 441 342 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (i.e.,)show 441 358 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn 1.26510 0. 32 0.12651 0.( C-Linda [SCA90] on a network of)awidthshow 452 79 gm 0.90667 0. 32 0.09066 0.(workstations. We have developed a chess-oriented software library based on a publicly available)awidthshow 463 79 gm 0.73593 0. 32 0.07359 0.(program, namely GNUChess \(courtesy of Open Software Foundation\). Using these tools we have)awidthshow 474 79 gm 0.55084 0. 32 0.05508 0.(built several parallel playing programs, embedding different parallel search algorithms; in order to)awidthshow 485 79 gm 1.41540 0. 32 0.14154 0.(simplify comparison with results reported in other papers, our experiments were made using a)awidthshow 496 79 gm (standard set of tests [BraKop82].)show 507 79 gm 0.30136 0. 32 0.03013 0.(This paper has the following structure: in Sect. 2 we define the concept of static and dynamic game)awidthshow 518 79 gm 0.22994 0. 32 0.02299 0.(tree splitting; in Sect. 3 we discuss how parallel search algorithms can be programmed in Linda; we)awidthshow 529 79 gm 0.27206 0. 32 0.02720 0.(summarise our experiments on static splitting algorithms in Sect.4, whereas Sect.5 contains data for)awidthshow 540 79 gm 0.39337 0. 32 0.03933 0.(dynamic splitting algorithms. In Sect.6 we make a number of comparisons with results obtained by)awidthshow 551 79 gm (other researchers.)show 581 79 gm 1 fs 12 fz bu fc 2 F /|______Times-Bold fnt bn (2. A classification of splitting criteria)show 594 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.18798 0. 32 0.01879 0.(There are several ways for handling a game tree during a parallel search, that basically differ for the)awidthshow 605 79 gm 0.64132 0. 32 0.06413 0.(splitting rules they use. We define some concepts in order to highlight properties of such splitting)awidthshow 616 79 gm (rules. Consider the following definitions:)show 628 88 gm 1 fs bu fc 2 F /|______Times-Bold fnt bn (Def)show 628 104 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.72631 0. 32 0.07263 0.(. )awidthshow 628 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.00660 0.(Splitting)ashow 628 147 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.59432 0. 32 0.05943 0.(: Let A be a game tree and N={N)awidthshow 628 300 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.20324 0.(1)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.50598 0. 32 0.05059 0.(, N)awidthshow 628 318 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.19212 0.(2)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.49163 0. 32 0.04916 0.(, \311, N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.19212 0.(n)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.56747 0. 32 0.05674 0.(} its set of nodes; let P={P)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.19212 0.(1)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.41320 0. 32 0.04132 0.(, P)awidthshow 628 494 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.15512 0.(2)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.51040 0. 32 0.05104 0.(, \311,)awidthshow 643 101 gm (P)show 643 107 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.10221 0.(m)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.17745 0. 32 0.01774 0.(} a set of processes. A )awidthshow 643 216 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.00639 0.(splitting)ashow 643 252 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.19348 0. 32 0.01934 0.( for A in P is a function D:N)awidthshow 643 379 gm bu fc {}mark F /Symbol /|______Symbol 0 rf bn bu fc 2 F /|______Symbol fnt bn 0.12472 0.(\256)ashow bu fc 2 F /|______Times-Roman fnt bn 0.17547 0. 32 0.01754 0.(P which maps each node of A)awidthshow 655 101 gm (to a process in P.)show 668 88 gm 1 fs bu fc 2 F /|______Times-Bold fnt bn (Def)show 668 104 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.82168 0. 32 0.08216 0.(. )awidthshow 668 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 1.02569 0. 32 0.10256 0.(Explorer and supervisor processes)awidthshow 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.49407 0. 32 0.04940 0.(: Let D be a splitting for the game tree A to the set P of)awidthshow 683 101 gm 1.24938 0. 32 0.12493 0.(processes; let N be the nodes of A and N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.22651 0.(i)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 1.26876 0. 32 0.12687 0.( a generic node \(N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.22651 0.(i)ashow 11 fz bu fc 2 F /|______Symbol fnt bn 0.71040 0.(\316)ashow bu fc 2 F /|______Times-Roman fnt bn 1.18743 0. 32 0.11874 0.(N\). We call )awidthshow 683 454 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.00755 0.(explorer)ashow 683 491 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn 1.53289 0. 32 0.15328 0.( of N)awidthshow 683 517 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (i)show 699 101 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.35369 0. 32 0.03536 0.(\(according to D\) the process D\(N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn (i)show 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.30151 0. 32 0.03015 0.(\). Moreover, let )awidthshow 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.10374 0.(father)ashow 699 351 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.48904 0. 32 0.04890 0.(: N)awidthshow 699 365 gm bu fc 2 F /|______Symbol fnt bn 0.25772 0.(\256)ashow bu fc 2 F /|______Times-Roman fnt bn 0.36575 0. 32 0.03657 0.(N be a function that associates a)awidthshow 711 101 gm 1.37420 0. 32 0.13742 0.(node with its predecessor node \(we define the root node as predecessor of itself\); we call)awidthshow 722 101 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (supervisor)show 722 147 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn ( of N)show 9 fz bu fc 2 F /|______Times-Roman fnt bn (i)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( \(according to D\) the process D\(father\(N)show 9 fz bu fc 2 F /|______Times-Roman fnt bn (i)show 11 fz bu fc 2 F /|______Times-Roman fnt bn (\)\).)show 734 79 gm 0.84487 0. 32 0.08448 0.(After a splitting the evaluation of a subtree is assigned to a specific process named )awidthshow 734 464 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.00755 0.(explorer)ashow 734 501 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.94177 0. 32 0.09417 0.(. For)awidthshow 745 79 gm 0.42999 0. 32 0.04299 0.(instance, let \(N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.05787 0.(i)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.10260 0.(,P)ashow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.05787 0.(j)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.25680 0. 32 0.02568 0.(\) be a pair in D; since N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.05787 0.(i)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.36682 0. 32 0.03668 0.( fully identifies the subtree S)awidthshow 745 397 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.07580 0.(i)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.35919 0. 32 0.03591 0.( of which it is the root, the)awidthshow F T cp %%Page: ? 5 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 336 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Helvetica fnt bn (A Comparison of Parallel Search Algorithms)show 773 79 gm (UBLCS-94-14)show 773 519 gm (3)show 118 79 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.13336 0. 32 0.01333 0.(minimax value for subtree S)awidthshow 118 204 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (i)show 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.13778 0. 32 0.01377 0.( must be computed by explorer P)awidthshow 118 352 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (j)show 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.13641 0. 32 0.01364 0.(. To evaluate a subtree S)awidthshow 118 463 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (i)show 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.12878 0. 32 0.01287 0.( the explorer)awidthshow 129 79 gm (P)show 129 85 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.07980 0. 32 0.00798 0.(j )awidthshow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.32028 0. 32 0.03202 0.(has to know the minimax values of the subtrees whose roots are the successors of N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.05039 0.(i)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.34561 0. 32 0.03456 0.(; function D)awidthshow 140 79 gm 0.05783 0. 32 0.00578 0.(defines an explorer for each of such subtrees as well. Let N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn (s)show 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.03936 0. 32 0.00393 0.( be one of N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn (i)show 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.06500 0. 32 0.00650 0.(\325s successors and P)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn (s)show 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.02426 0.(=D\(N)ashow 9 fz bu fc 2 F /|______Times-Roman fnt bn (s)show 11 fz bu fc 2 F /|______Times-Roman fnt bn (\))show 151 79 gm 0.24230 0. 32 0.02423 0.(the corresponding explorer. Which relation is established between P)awidthshow 151 382 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.06809 0.(j)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.29953 0. 32 0.02995 0.( and P)awidthshow 151 412 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.05468 0.(s)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.26626 0. 32 0.02662 0.(? There is a dependence)awidthshow 162 79 gm 0.83358 0. 32 0.08335 0.(of P)awidthshow 162 98 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.20744 0.(s)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.75210 0. 32 0.07521 0.( from P)awidthshow 162 136 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.12579 0.(j)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.79711 0. 32 0.07971 0.( because the minimax value of the subtree assigned to P)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.17608 0.(s)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.52780 0. 32 0.05278 0.( is used by P)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.12579 0.(j)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.56365 0. 32 0.05636 0.(, and P)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.17608 0.(s)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.86746 0. 32 0.08674 0.( must)awidthshow 173 79 gm (report to this process. We call P)show 173 219 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (j)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( )show 2 fs bu fc 2 F /|______Times-Italic fnt bn (supervisor)show 173 269 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn ( of N)show 9 fz bu fc 2 F /|______Times-Roman fnt bn (s)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( because it manages Ns\325minimax value.)show 184 79 gm 0.04608 0. 32 0.00460 0.(Thus, a game tree splitting establishes a hierarchic relationship among processes. Such a relationship)awidthshow 195 79 gm -0.00288 0.(changes dynamically \(i.e., during the tree visit\) depending on the relationship among subtrees visited)ashow 206 79 gm 0.55511 0. 32 0.05551 0.(by the processes at any time. In fact, it may happen that, in a subsequent stage of the visit, P)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.09809 0.(i)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.55648 0. 32 0.05564 0.( will)awidthshow 217 79 gm 0.85998 0. 32 0.08599 0.(have to communicate to P)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.16860 0.(s)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.69030 0. 32 0.06903 0.( the result of its search because the subtree it visited is included in the)awidthshow 228 79 gm (subtree explored by P)show 9 fz bu fc 2 F /|______Times-Roman fnt bn (s)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( .)show (nc 252 109 454 494 6 rc)kp 0 gr 254.5 266.5 279.5 292.5 0 ov 270 270 gm (nc 260 269 272 291 6 rc)kp F 1 setTxMode %%BeginFont: Geneva bu fc 22 0 -6 30 24 bb 218 array /CharData mdf <001C00000000 FF1CFFFF0000 001C00000000 001C00000000 001C00000000 001C00000000 FF1CFFFF0000 FF1CFFFF0000 FF1CFFFF0000 001C10100000 FF1CFFFF0000 FF1CFFFF0000 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2140 1E40 0040 0040 0040 4080 2100 1E00 0000 0000 >cdf 102< 0000 0000 0E00 1100 2000 2000 FC00 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 0000 0000 >cdf 101< 0000 0000 1E00 2100 4080 4080 8040 8040 FFC0 8000 8000 8000 4000 4080 2100 1E00 0000 0000 >cdf 100< 0000 0000 0040 0040 0040 0040 1E40 2140 40C0 4040 8040 8040 8040 8040 8040 8040 4040 40C0 2140 1E40 0000 0000 >cdf 99< 0000 0000 1F00 2080 4040 4000 8000 8000 8000 8000 8000 8000 4000 4040 2080 1F00 0000 0000 >cdf 98< 0000 0000 8000 8000 8000 8000 9E00 A100 C080 8080 8040 8040 8040 8040 8040 8040 8080 C080 A100 9E00 0000 0000 >cdf 97< 0000 0000 1F00 6080 8040 0040 00C0 0340 0C40 3040 4040 8040 8040 80C0 4340 3C40 0000 0000 >cdf 96< 0000 0000 8000 4000 2000 1000 0000 0000 >cdf 95< 00000000 00000000 FFFF0000 00000000 00000000 >cdf 94< 0000 0000 3000 4800 8400 0000 0000 >cdf 93< 0000 0000 F000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 F000 0000 0000 >cdf 92< 0000 0000 8000 8000 4000 4000 2000 2000 1000 1000 0800 0800 0400 0400 0200 0200 0100 0100 0080 0080 0040 0040 0000 0000 >cdf 91< 0000 0000 F000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 F000 0000 0000 >cdf 90< 0000 0000 FFC0 0040 0080 0080 0100 0200 0200 0400 0400 0800 0800 1000 2000 2000 4000 4000 8000 FFC0 0000 0000 >cdf 89< 0000 0000 8020 8020 4040 4040 2080 2080 1100 1100 0A00 0A00 0400 0400 0400 0400 0400 0400 0400 0400 0000 0000 >cdf 88< 0000 0000 8020 8020 4040 4040 2080 1100 1100 0A00 0400 0400 0A00 1100 1100 2080 4040 4040 8020 8020 0000 0000 >cdf 87< 00000000 00000000 80002000 80002000 80002000 40404000 40404000 40404000 20A08000 20A08000 20A08000 11110000 11110000 11110000 0A0A0000 0A0A0000 0A0A0000 04040000 04040000 04040000 00000000 00000000 >cdf 86< 0000 0000 8008 8008 4010 4010 4010 2020 2020 2020 1040 1040 1040 0880 0880 0880 0500 0500 0200 0200 0000 0000 >cdf 85< 0000 0000 8010 8010 8010 8010 8010 8010 8010 8010 8010 8010 8010 8010 8010 8010 4020 4020 30C0 0F00 0000 0000 >cdf 84< 0000 0000 FFF8 0200 0200 0200 0200 0200 0200 0200 0200 0200 0200 0200 0200 0200 0200 0200 0200 0200 0000 0000 >cdf 83< 0000 0000 3F80 4040 8020 8000 8000 8000 6000 1F00 00C0 0020 0020 0010 0010 0010 8020 8020 60C0 1F00 0000 0000 >cdf 82< 0000 0000 FF00 80C0 8020 8020 8010 8010 8010 8020 8020 80C0 FF80 8080 8040 8040 8020 8020 8010 8010 0000 0000 >cdf 81< 0000 0000 0700 18C0 2020 4010 4010 8008 8008 8008 8008 8008 8008 8008 8008 4090 4050 2020 18D0 0708 0000 0000 >cdf 80< 0000 0000 FE00 8180 8040 8040 8020 8020 8020 8020 8040 8040 8180 FE00 8000 8000 8000 8000 8000 8000 0000 0000 >cdf 79< 0000 0000 0700 18C0 2020 4010 4010 8008 8008 8008 8008 8008 8008 8008 8008 4010 4010 2020 18C0 0700 0000 0000 >cdf 78< 0000 0000 8010 C010 C010 A010 A010 9010 8810 8810 8410 8210 8210 8110 8090 8090 8050 8030 8030 8010 0000 0000 >cdf 77< 00000000 00000000 80020000 C0060000 A00A0000 90120000 88220000 84420000 82820000 81020000 80020000 80020000 80020000 80020000 80020000 80020000 80020000 80020000 80020000 80020000 00000000 00000000 >cdf 76< 0000 0000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 FFC0 0000 0000 >cdf 75< 0000 0000 8010 8020 8040 8080 8100 8200 8400 8800 9000 A800 C400 8200 8100 8080 8040 8020 8010 8008 0000 0000 >cdf 74< 0000 0000 0010 0010 0010 0010 0010 0010 0010 0010 0010 0010 0010 0010 8010 8010 8020 4020 30C0 0F00 0000 0000 >cdf 73< 0000 0000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 0000 0000 >cdf 72< 0000 0000 8010 8010 8010 8010 8010 8010 8010 8010 FFF0 8010 8010 8010 8010 8010 8010 8010 8010 8010 0000 0000 >cdf 71< 0000 0000 0F80 3040 4020 4000 8000 8000 8000 8000 83F0 8010 8010 8010 8010 8010 4020 4020 30C0 0F00 0000 0000 >cdf 70< 0000 0000 FFC0 8000 8000 8000 8000 8000 8000 8000 FF00 8000 8000 8000 8000 8000 8000 8000 8000 8000 0000 0000 >cdf 69< 0000 0000 FFC0 8000 8000 8000 8000 8000 8000 8000 FF00 8000 8000 8000 8000 8000 8000 8000 8000 FFC0 0000 0000 >cdf 68< 0000 0000 FE00 8180 8040 8020 8020 8010 8010 8010 8010 8010 8010 8010 8010 8020 8020 8040 8180 FE00 0000 0000 >cdf 67< 0000 0000 0FC0 3020 4010 4000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 4000 4010 3020 0FC0 0000 0000 >cdf 66< 0000 0000 FF80 8040 8020 8020 8020 8020 8040 FF80 8040 8020 8010 8010 8010 8010 8010 8020 8040 FF80 0000 0000 >cdf 65< 00000000 00000000 01000000 01000000 01000000 02800000 02800000 04400000 04400000 08200000 08200000 10100000 10100000 3FF80000 20080000 20080000 40040000 40040000 80020000 80020000 00000000 00000000 >cdf 64< 00000000 00000000 07C00000 18300000 20080000 40040000 43C40000 84220000 88220000 88220000 88220000 88220000 84640000 43980000 40000000 20000000 18000000 07C00000 00000000 00000000 >cdf 63< 0000 0000 1F80 2040 4020 8020 8020 0020 0040 0080 0100 0200 0200 0400 0400 0400 0000 0000 0400 0400 0000 0000 >cdf 62< 0000 0000 8000 4000 2000 1000 0800 0400 0200 0400 0800 1000 2000 4000 8000 0000 0000 >cdf 61< 0000 0000 FFC0 0000 0000 0000 FFC0 0000 0000 >cdf 60< 0000 0000 0200 0400 0800 1000 2000 4000 8000 4000 2000 1000 0800 0400 0200 0000 0000 >cdf 59< 0000 0000 2000 2000 0000 0000 0000 0000 0000 0000 0000 0000 6000 2000 2000 2000 4000 8000 0000 0000 >cdf 58< 0000 0000 8000 8000 0000 0000 0000 0000 0000 0000 0000 0000 8000 8000 0000 0000 >cdf 57< 0000 0000 0F00 30C0 4020 4020 8010 8010 8010 8010 4010 4030 30D0 0F10 0010 0020 0020 0040 0180 1E00 0000 0000 >cdf 56< 0000 0000 1F80 2040 4020 4020 4020 4020 2040 1F80 2040 4020 4020 8010 8010 8010 4020 4020 30C0 0F00 0000 0000 >cdf 55< 0000 0000 FFF0 0010 0010 0020 0020 0040 0040 0080 0080 0100 0100 0200 0200 0400 0400 0800 0800 0800 0000 0000 >cdf 54< 0000 0000 07C0 1800 2000 4000 4000 8000 8F00 B0C0 C020 8020 8010 8010 8010 8010 4020 4020 30C0 0F00 0000 0000 >cdf 53< 0000 0000 FFE0 8000 8000 8000 8000 8000 FF00 00C0 0020 0020 0010 0010 0010 0010 0020 8020 60C0 1F00 0000 0000 >cdf 52< 0000 0000 0010 0030 0050 0090 0110 0210 0410 0810 1010 2010 4010 8010 FFFC 0010 0010 0010 0010 0010 0000 0000 >cdf 51< 0000 0000 FFF0 0020 0040 0080 0100 0200 0700 0080 0040 0040 0020 0020 0020 0020 0040 8040 6180 1E00 0000 0000 >cdf 50< 0000 0000 0F80 3040 4020 8010 8010 0010 0010 0020 0040 0080 0100 0200 0400 0800 1000 2000 4000 FFF0 0000 0000 >cdf 49< 0000 0000 2000 6000 A000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 0000 0000 >cdf 48< 0000 0000 0F00 1080 2040 4020 4020 8010 8010 8010 8010 8010 8010 8010 8010 4020 4020 2040 1080 0F00 0000 0000 >cdf 47< 0000 0000 0080 0080 0100 0100 0200 0200 0400 0400 0800 0800 1000 1000 2000 2000 4000 4000 8000 8000 0000 0000 >cdf 46< 0000 0000 8000 8000 0000 0000 >cdf 45< 0000 0000 FFC0 0000 0000 >cdf 44< 0000 0000 6000 2000 2000 2000 4000 8000 0000 0000 >cdf 43< 0000 0000 0800 0800 0800 0800 FF80 0800 0800 0800 0800 0000 0000 >cdf 42< 0000 0000 2010 1020 0840 0480 0300 FFFC 0300 0480 0840 1020 2010 0000 0000 >cdf 41< 0000 0000 8000 4000 2000 2000 1000 1000 0800 0800 0800 0800 0800 0800 0800 0800 1000 1000 2000 2000 4000 8000 0000 0000 >cdf 40< 0000 0000 0800 1000 2000 2000 4000 4000 8000 8000 8000 8000 8000 8000 8000 8000 4000 4000 2000 2000 1000 0800 0000 0000 >cdf 39< 0000 0000 8000 8000 8000 8000 0000 0000 >cdf 38< 00000000 00000000 0E000000 11000000 20800000 20800000 21000000 22000000 14000000 08000000 14000000 22000000 41040000 40880000 80500000 80200000 80500000 40880000 21040000 1E020000 00000000 00000000 >cdf 37< 0000 0000 37F8 4804 8404 8408 8410 8420 4840 3080 0100 0200 0430 0848 1084 2084 2084 4084 4048 4030 0000 0000 >cdf 36< 0000 0000 0800 0800 3E00 4900 8880 8880 8800 4800 2800 1800 0C00 0A00 0900 0880 0880 0880 8880 8880 4900 3E00 0800 0800 0000 0000 >cdf 35< 0000 0000 0220 0220 3FFC 0440 0440 0880 0880 FFF0 1100 1100 0000 0000 >cdf 34< 0000 0000 8800 8800 8800 8800 0000 0000 >cdf 33< 0000 0000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 8000 0000 0000 8000 8000 0000 0000 >cdf /|______Geneva bf bn %%EndFont 9 fz bu fc 2 F /|______Geneva fnt bn -0.33325 0.(Root)ashow (nc 252 109 454 494 6 rc)kp 0 gr 309.5 142.5 334.5 167.5 0 ov 365.5 111.5 391.5 136.5 0 ov 367.5 174.5 392.5 199.5 0 ov 365 123 gm 334 154 lin 367 186 lin 310.5 266.5 336.5 292.5 0 ov 426.5 391.5 452.5 417.5 0 ov 428.5 454.5 453.5 480.5 0 ov 426 403 gm 395 434 lin 428 467 lin 312.5 390.5 337.5 415.5 0 ov 368.5 359.5 394.5 384.5 0 ov 370.5 422.5 395.5 447.5 0 ov 368 371 gm 337 402 lin 370 434 lin 279 279 gm 310 279 lin 279 279 gm 311 402 lin 309 154 gm 279 279 lin 382 140 gm (nc 374 139 385 150 6 rc)kp F 1 setTxMode bu fc 2 F /|______Helvetica fnt bn (P)show 6 fz bu fc 2 F /|______Helvetica fnt bn (4)show 383 203 gm (nc 375 202 386 214 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 7 fz bu fc 2 F /|______Helvetica fnt bn (3)show 382 182 gm (nc 374 181 385 197 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (32)show 381 118 gm (nc 373 117 384 133 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (31)show 441 397 gm (nc 433 396 444 412 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (41)show 442 461 gm (nc 434 460 445 476 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (42)show 383 366 gm (nc 375 365 386 381 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (35)show 384 428 gm (nc 376 427 387 443 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (36)show 325 149 gm (nc 317 148 328 164 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (21)show 326 273 gm (nc 318 272 329 288 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (22)show 325 397 gm (nc 317 396 328 412 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (23)show 269 297 gm (nc 261 296 272 307 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 6 fz bu fc 2 F /|______Helvetica fnt bn (1)show 326 170 gm (nc 318 169 329 180 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 6 fz bu fc 2 F /|______Helvetica fnt bn (4)show 443 483 gm (nc 435 482 446 493 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 6 fz bu fc 2 F /|______Helvetica fnt bn (3)show 326 418 gm (nc 318 417 329 429 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 7 fz bu fc 2 F /|______Helvetica fnt bn (2)show 383 450 gm (nc 375 449 386 461 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 7 fz bu fc 2 F /|______Helvetica fnt bn (3)show 326 296 gm (nc 318 295 329 307 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 7 fz bu fc 2 F /|______Helvetica fnt bn (1)show 443 420 gm (nc 435 419 446 431 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 7 fz bu fc 2 F /|______Helvetica fnt bn (2)show 382 387 gm (nc 374 386 385 398 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 7 fz bu fc 2 F /|______Helvetica fnt bn (2)show (nc 252 109 454 494 6 rc)kp 0 gr 368.5 299.5 394.5 325.5 0 ov 367 248 gm 336 279 lin 368 312 lin 382 242 gm (nc 374 241 385 257 6 rc)kp F 1 setTxMode 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (33)show 383 306 gm (nc 375 305 386 321 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (34)show 384 328 gm (nc 376 327 387 338 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 6 fz bu fc 2 F /|______Helvetica fnt bn (2)show 383 265 gm (nc 375 264 386 276 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 7 fz bu fc 2 F /|______Helvetica fnt bn (1)show (nc 252 109 454 494 6 rc)kp 0 gr 367.5 235.5 392.5 261.5 0 ov 241 77 gm (nc 30 28 811 566 6 rc)kp 241 525 lin 482 240 gm F 1 setTxMode 11 fz bu fc 2 F /|______Times-Roman fnt bn (Fig.1 )show 1 fs bu fc 2 F /|______Times-Bold fnt bn (Splitting a game tree)show 500 77 gm 0 gr 500 525 lin 519 79 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.25543 0. 32 0.02554 0.(Fig.1 shows a game tree splitting; nodes are labelled with the name of the explorer of the subtree of)awidthshow 530 79 gm 0.64910 0. 32 0.06491 0.(which they are root. Some processes are explorers of several subtrees; nevertheless, at any instant)awidthshow 541 79 gm 1.11099 0. 32 0.11109 0.(during the search, they will be engaged in the visit of no more than one subtree. Therefore, the)awidthshow 552 79 gm 0.66833 0. 32 0.06683 0.(description of a splitting should include the visit order followed by each process; this information)awidthshow 563 79 gm 0.02639 0. 32 0.00263 0.(represents the \322dynamic\323 component of the splitting. In Fig.2 it is shown an example \(with reference)awidthshow 574 79 gm (to the game tree in Fig.1\).)show 614 228 gm (nc 601 227 669 383 6 rc)kp 12 fz bu fc 2 F /|______Helvetica fnt bn (P)show 9 fz bu fc 2 F /|______Helvetica fnt bn (1)show 12 fz bu fc 2 F /|______Helvetica fnt bn (: N)show 9 fz bu fc 2 F /|______Helvetica fnt bn (33)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 614 278 gm bu fc 2 F /|______Helvetica fnt bn (N)show 614 287 gm 9 fz bu fc 2 F /|______Helvetica fnt bn (22)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 614 309 gm bu fc 2 F /|______Helvetica fnt bn (Root)show 631 228 gm (P)show 9 fz bu fc 2 F /|______Helvetica fnt bn (2)show 12 fz bu fc 2 F /|______Helvetica fnt bn (: N)show 9 fz bu fc 2 F /|______Helvetica fnt bn (35)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 631 278 gm bu fc 2 F /|______Helvetica fnt bn (N)show 631 287 gm 9 fz bu fc 2 F /|______Helvetica fnt bn (41)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 631 309 gm bu fc 2 F /|______Helvetica fnt bn (N)show 9 fz bu fc 2 F /|______Helvetica fnt bn (23)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 631 339 gm bu fc 2 F /|______Helvetica fnt bn (N)show 631 348 gm 9 fz bu fc 2 F /|______Helvetica fnt bn (34)show 648 228 gm 12 fz bu fc 2 F /|______Helvetica fnt bn (P)show 9 fz bu fc 2 F /|______Helvetica fnt bn (3)show 12 fz bu fc 2 F /|______Helvetica fnt bn (: N)show 9 fz bu fc 2 F /|______Helvetica fnt bn (32)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 648 278 gm bu fc 2 F /|______Helvetica fnt bn (N)show 648 287 gm 9 fz bu fc 2 F /|______Helvetica fnt bn (42)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 648 309 gm bu fc 2 F /|______Helvetica fnt bn (N)show 9 fz bu fc 2 F /|______Helvetica fnt bn (36)show 665 228 gm 12 fz bu fc 2 F /|______Helvetica fnt bn (P)show 9 fz bu fc 2 F /|______Helvetica fnt bn (4)show 12 fz bu fc 2 F /|______Helvetica fnt bn (: N)show 9 fz bu fc 2 F /|______Helvetica fnt bn (31)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 665 278 gm bu fc 2 F /|______Helvetica fnt bn (N)show 665 287 gm 9 fz bu fc 2 F /|______Helvetica fnt bn (21)show (nc 598 218 671 384 6 rc)kp 0 gr 600.5 220.5 670.5 362.5 0 rc 587 77 gm (nc 30 28 811 566 6 rc)kp 587 525 lin 699 186 gm F 1 setTxMode 11 fz bu fc 2 F /|______Times-Roman fnt bn (Fig.2)show 1 fs bu fc 2 F /|______Times-Bold fnt bn ( Splitting: evaluation order by every process)show 717 77 gm 0 gr 717 525 lin 736 79 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn 1.19064 0. 32 0.11906 0.(In general, it is impossible to fix the visiting order of every subtree, because it depends on the)awidthshow 747 79 gm 0.00778 0. 32 0.00077 0.(processes\325 relative speeds. Nevertheless, there are some synchronisation points marking the stages of)awidthshow F T cp %%Page: ? 6 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 336 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Helvetica fnt bn (A Comparison of Parallel Search Algorithms)show 773 79 gm (UBLCS-94-14)show 773 519 gm (4)show 118 79 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.19485 0. 32 0.01948 0.(the visit: a process can completely search a subtree S only after having received the minimax values)awidthshow 129 79 gm 1.06338 0. 32 0.10633 0.(of all S\325subtrees. Fig.3 depicts a snapshot of the search of game tree in Fig.1, with the splitting)awidthshow 140 79 gm (specified in Fig.2.)show 185 369 gm (nc 172 368 240 502 6 rc)kp 12 fz bu fc 2 F /|______Helvetica fnt bn (P)show 9 fz bu fc 2 F /|______Helvetica fnt bn (1)show 12 fz bu fc 2 F /|______Helvetica fnt bn (: N)show 9 fz bu fc 2 F /|______Helvetica fnt bn (33)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 185 419 gm bu fc 2 F /|______Helvetica fnt bn (N)show 185 428 gm 9 fz bu fc 2 F /|______Helvetica fnt bn (22)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 185 450 gm bu fc 2 F /|______Helvetica fnt bn (Root)show 202 369 gm (P)show 9 fz bu fc 2 F /|______Helvetica fnt bn (2)show 12 fz bu fc 2 F /|______Helvetica fnt bn (: N)show 9 fz bu fc 2 F /|______Helvetica fnt bn (35)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 202 419 gm bu fc 2 F /|______Helvetica fnt bn (N)show 202 428 gm 9 fz bu fc 2 F /|______Helvetica fnt bn (41)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 202 450 gm bu fc 2 F /|______Helvetica fnt bn (N)show 9 fz bu fc 2 F /|______Helvetica fnt bn (23)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 202 480 gm bu fc 2 F /|______Helvetica fnt bn (N)show 202 489 gm 9 fz bu fc 2 F /|______Helvetica fnt bn (34)show 219 369 gm 12 fz bu fc 2 F /|______Helvetica fnt bn (P)show 9 fz bu fc 2 F /|______Helvetica fnt bn (3)show 12 fz bu fc 2 F /|______Helvetica fnt bn (: N)show 9 fz bu fc 2 F /|______Helvetica fnt bn (32)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 219 419 gm bu fc 2 F /|______Helvetica fnt bn (N)show 219 428 gm 9 fz bu fc 2 F /|______Helvetica fnt bn (42)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 219 450 gm bu fc 2 F /|______Helvetica fnt bn (N)show 9 fz bu fc 2 F /|______Helvetica fnt bn (36)show 236 369 gm 12 fz bu fc 2 F /|______Helvetica fnt bn (P)show 9 fz bu fc 2 F /|______Helvetica fnt bn (4)show 12 fz bu fc 2 F /|______Helvetica fnt bn (: N)show 9 fz bu fc 2 F /|______Helvetica fnt bn (31)show 12 fz bu fc 2 F /|______Symbol fnt bn (\256)show 236 419 gm bu fc 2 F /|______Helvetica fnt bn (N)show 236 428 gm 9 fz bu fc 2 F /|______Helvetica fnt bn (21)show (nc 164 97 366 505 6 rc)kp 0 gr 171.5 361.5 241.5 503.5 0 rc 2 2 pen 224 389 gm 237 402 lin 237 388 gm 224 401 lin 224 420 gm 237 432 lin 237 419 gm 224 432 lin 190 390 gm 203 403 lin 203 389 gm 190 402 lin 174 389 gm 187 402 lin 187 388 gm 174 401 lin 207 420 gm 219 432 lin 219 419 gm 207 432 lin 207 389 gm 219 402 lin 219 388 gm 207 401 lin 1 1 pen 166.5 169.5 191.5 195.5 0 ov 182 174 gm (nc 172 173 184 195 6 rc)kp F 1 setTxMode bu fc 2 F /|______Geneva fnt bn -0.33325 0.(Root)ashow 2 2 pen (nc 164 97 366 505 6 rc)kp 0 gr 222 169 248 195 0 ov 338 275 364 301 0 ov 1 1 pen 338 287 gm 307 318 lin 0 0 2 9 12 2 dh 340 351 lin rh psb pse 224.5 274.5 249.5 299.5 0 ov 2 2 pen 282 306 307 331 0 ov 0 0 2 9 5 2 dh 1 1 pen 280 255 gm 249 286 lin rh psb pse 282 318 lin 191 182 gm 222 182 lin 191 183 gm 223 286 lin 0 0 2 9 5 2 dh 232 99 gm 191 182 lin rh psb pse 353 281 gm (nc 345 280 356 296 6 rc)kp F 1 setTxMode bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (41)show 296 312 gm (nc 288 311 299 328 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (36)show 238 176 gm (nc 230 175 241 191 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (22)show 237 281 gm (nc 229 280 240 296 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (23)show 181 200 gm (nc 173 199 184 210 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 6 fz bu fc 2 F /|______Helvetica fnt bn (1)show 238 302 gm (nc 230 301 241 313 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 7 fz bu fc 2 F /|______Helvetica fnt bn (2)show 295 334 gm (nc 287 333 298 345 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 7 fz bu fc 2 F /|______Helvetica fnt bn (3)show 238 199 gm (nc 230 198 241 210 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 7 fz bu fc 2 F /|______Helvetica fnt bn (1)show 355 304 gm (nc 347 303 358 315 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 7 fz bu fc 2 F /|______Helvetica fnt bn (2)show (nc 164 97 366 505 6 rc)kp 0 gr 280.5 202.5 306.5 228.5 0 ov 0 0 2 9 5 2 dh 279 151 gm 248 182 lin rh psb pse 280 215 lin 295 209 gm (nc 287 208 298 225 6 rc)kp F 1 setTxMode 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (34)show 296 231 gm (nc 288 230 299 241 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 6 fz bu fc 2 F /|______Helvetica fnt bn (2)show 153 77 gm (nc 30 28 811 566 6 rc)kp 0 gr 153 525 lin 394 202 gm F 1 setTxMode 11 fz bu fc 2 F /|______Times-Roman fnt bn (Fig.3 )show 1 fs bu fc 2 F /|______Times-Bold fnt bn (Snapshot of a splitting during search)show 412 77 gm 0 gr 412 525 lin 431 79 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn 1.40029 0. 32 0.14002 0.(In Fig.3 process P)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.38081 0.(4)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 1.14730 0. 32 0.11473 0.( is idle because it has completed its own list of tasks; P)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.38081 0.(1)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 1.08932 0. 32 0.10893 0.( is waiting for N)awidthshow 431 512 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (34)show 442 79 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.39398 0. 32 0.03939 0.(minimax value from process P)awidthshow 442 216 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.12751 0.(2)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.46432 0. 32 0.04643 0.(; likewise, P)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.12751 0.(3)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.35842 0. 32 0.03584 0.( is waiting for N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.12751 0.(41)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.40191 0. 32 0.04019 0.( value from P)awidthshow 442 423 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.12092 0.(2)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.47790 0. 32 0.04779 0.(. Therefore, P)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.12092 0.(2)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.27145 0. 32 0.02714 0.( is the)awidthshow 453 79 gm 0.43975 0. 32 0.04397 0.(only process working at present: it is evaluating N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.11721 0.(41)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.42282 0. 32 0.04228 0.(. There is a hierarchic relation between P)awidthshow 453 499 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.13636 0.(3)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.43426 0. 32 0.04342 0.( and)awidthshow 464 79 gm (P)show 464 85 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (2)show 11 fz bu fc 2 F /|______Times-Roman fnt bn (: it will be reversed when, having completed N)show 464 295 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (36)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( evaluation, P)show 464 364 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (3)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( sends a message to P)show 464 463 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (2)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( .)show 475 79 gm 0.93658 0. 32 0.09365 0.(The main problem in searching a game tree by a splitting method is to decide when the subtree)awidthshow 475 520 gm (-)show 486 79 gm 1.91757 0. 32 0.19175 0.(process association should be established. Usually, it makes no sense to allocate subtrees to)awidthshow 497 79 gm (processes before search starts, because of the following reasons:)show 509 88 gm (\245 it is necessary to know the whole tree;)show 526 88 gm 1.29272 0. 32 0.12927 0.(\245 the\312)awidthshow 526 112 gm bu fc 2 F /|______Symbol fnt bn 0.49502 0.(ab)ashow bu fc 2 F /|______Times-Roman fnt bn 1.19796 0. 32 0.11979 0.( algorithm property of cutting subtrees makes useless the visit of some of them. It is)awidthshow 538 101 gm 0.39840 0. 32 0.03984 0.(impossible to determine )awidthshow 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.39581 0. 32 0.03958 0.(a priori)awidthshow 538 245 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.45089 0. 32 0.04508 0.( the identity of these subtrees and then to obtain at run-time a)awidthshow 549 101 gm (uniform load distribution.)show 561 79 gm 1.13494 0. 32 0.11349 0.(At search time we usually have the following scenery: some "lucky" processes complete search)awidthshow 572 79 gm 0.15518 0. 32 0.01551 0.(before others \()awidthshow 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.03363 0.(e.g.)ashow 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.14312 0. 32 0.01431 0.(, because of better cuts\) and will remain idle. Every solution for avoiding idleness)awidthshow 583 79 gm 1.27334 0. 32 0.12733 0.(must be dynamic, )awidthshow 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.33239 0.(i.e.)ashow 583 179 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn 1.44989 0. 32 0.14498 0.(, it must provide mechanisms able, during the search, to reassign to idle)awidthshow 594 79 gm 0.41198 0. 32 0.04119 0.(processes subtrees already assigned to overloaded processes. Therefore, a classification of splitting)awidthshow 605 79 gm 0.27206 0. 32 0.02720 0.(methods in static and dynamic is not really meaningful, because actually the only plausible solution)awidthshow 616 79 gm 0.58578 0. 32 0.05857 0.(is dynamic. On the other hand, it makes sense to distinguish different approaches according to the)awidthshow 627 79 gm (time they establish nodes where it will occur a splitting.)show 639 88 gm 1 fs bu fc 2 F /|______Times-Bold fnt bn (Def)show 639 104 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.78430 0. 32 0.07843 0.(. )awidthshow 639 110 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.40939 0. 32 0.04093 0.(Splitting node)awidthshow 639 172 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.72387 0. 32 0.07238 0.(: Let D be a splitting for game tree A; let N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.14743 0.(i)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.61416 0. 32 0.06141 0.( be a node of A; N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.14743 0.(i)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.34484 0. 32 0.03448 0.( is a )awidthshow 639 484 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.00639 0.(splitting)ashow 654 101 gm (node)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( \(according to D\) )show bu fc 2 F /|______Symbol fnt bn (\333 $)show bu fc 2 F /|______Times-Roman fnt bn (N)show 9 fz bu fc 2 F /|______Times-Roman fnt bn (j)show 11 fz bu fc 2 F /|______Times-Roman fnt bn (: N)show 654 242 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (i)show 11 fz bu fc 2 F /|______Times-Roman fnt bn (=father\(N)show 9 fz bu fc 2 F /|______Times-Roman fnt bn (j)show 11 fz bu fc 2 F /|______Times-Roman fnt bn (\) and D\(N)show 9 fz bu fc 2 F /|______Times-Roman fnt bn (j)show 11 fz bu fc 2 F /|______Times-Roman fnt bn (\))show currentfont SwToSym (\271)show setfont (D\(N)show 654 364 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (i)show 11 fz bu fc 2 F /|______Times-Roman fnt bn (\).)show 667 79 gm 0.38619 0. 32 0.03861 0.(A splitting node is one at which it is established the generation of a parallel search task, )awidthshow 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.11729 0.(i.e.)ashow 667 490 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.39413 0. 32 0.03941 0.(, where)awidthshow 678 79 gm 1.34124 0. 32 0.13412 0.(some of its subtrees are visited by processes different from its explorer. We can now state the)awidthshow 689 79 gm (following classification:)show 701 88 gm (\245 a )show 701 102 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (static)show 701 125 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn ( splitting algorithm decides all the splitting nodes before the search starts;)show 714 88 gm (\245 a )show 714 102 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (dynamic)show 714 139 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn ( algorithm decides some splitting nodes only during the search.)show 745 79 gm 1 fs 12 fz bu fc 2 F /|______Times-Bold fnt bn (3. Parallel search on a network of workstations)show F T cp %%Page: ? 7 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 336 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Helvetica fnt bn (A Comparison of Parallel Search Algorithms)show 773 79 gm (UBLCS-94-14)show 773 519 gm (5)show 118 79 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.48721 0. 32 0.04872 0.(High-level parallel programming languages are gaining momentum, because they simplify the task)awidthshow 129 79 gm 0.53451 0. 32 0.05345 0.(of building software for the novel architectures with several processors. Parallel search algorithms)awidthshow 140 79 gm (are good tests for these new languages.)show 151 79 gm 0.06134 0. 32 0.00613 0.(Parallel search algorithms have been programmed in several languages; for instance, in [ABD82] we)awidthshow 162 79 gm 0.90576 0. 32 0.09057 0.(find an algorithm based on semaphore primitives; in [Eli90] the Orca language was used. In this)awidthshow 173 79 gm 2.62359 0. 32 0.26235 0.(paper we will use Linda, a coordination language that consists of a small set of parallel)awidthshow 184 79 gm 0.30395 0. 32 0.03039 0.(programming primitives that can be added to any sequential language [CarGel90]. These primitives)awidthshow 195 79 gm (associatively access a )show 195 177 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (tuple space)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( shared among processes.)show 206 79 gm 0.74050 0. 32 0.07405 0.(There are several possible software architectures that can all be programmed in Linda; one of the)awidthshow 217 79 gm 0.73242 0. 32 0.07324 0.(most useful is the )awidthshow 217 163 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.15429 0.(master-worker)ashow 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.53817 0. 32 0.05381 0.( model. According to this model tasks created during the parallel)awidthshow 228 79 gm 0.18966 0. 32 0.01896 0.(evaluation of a program are dynamically distributed among processors. The parallel program should)awidthshow 239 79 gm (be structured as follows:)show 251 88 gm (\245 a )show 251 102 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (master)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( process generates tasks and coordinates the collection of solutions;)show 264 88 gm 0.61599 0. 32 0.06159 0.(\245 several identical )awidthshow 264 172 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (worker)show 264 203 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.63095 0. 32 0.06309 0.( processes pick and execute tasks and return task results to the master;)awidthshow 275 101 gm (when a task is terminated, a new task can be chosen;)show 288 88 gm 0.14007 0. 32 0.01400 0.(\245 in the tuple space there are two main kinds of tuples: active tuples for tasks \(we call this multiset)awidthshow 299 101 gm (the agenda\), and passive tuples that represent task results.)show 311 79 gm 1.13449 0. 32 0.11344 0.(The master)awidthshow 311 130 gm 1.33850 0. 32 0.13385 0.(-worker model allows to structure the supervisor of a node as a master process that)awidthshow 322 79 gm 0.12695 0. 32 0.01269 0.(coordinates several explorers as workers. This is simple to model: in the following program only the)awidthshow 333 79 gm (root is a splitting node.)show 340 78 gm (nc 336 79 348 525 6 rc)kp 0 gr 340 525 lin 368 97 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 10 fz bu fc 2 F /|______Courier fnt bn (int\312master_main\(int\312n_worker,int\312depth\))show 379 97 gm ({)show 390 97 gm (position\312*root,*successor;)show 401 97 gm (int\312nmoves,minimax,i,master\(\),worker\(\);)show 412 97 gm (for \(i=0;i0\)\))show 152 169 gm (/* more tasks in agenda and a worker is idle? */)show 163 133 gm ({ out\("job",subtree\); /* insert search task in agenda */)show 174 133 gm (free--;)show 185 133 gm (subtree++;)show 196 133 gm (})show 207 115 gm (else /* wait completion of a task */)show 218 133 gm ({)show 229 133 gm (in \("result",?value,?r_subtree\); /* get result */)show 240 133 gm (if \(value>local_score\) /* improved score? */)show 251 151 gm ({ local_score=value; /* local update of score */)show 262 151 gm (in \("score",?int\);)show 273 151 gm (out\("score",local_score\); /* global update of score */)show 284 151 gm (best=r_subtree;)show 295 151 gm (})show 306 133 gm (free++;})show 317 97 gm (in \("score",?int\); /* to avoid interference with next search */)show 329 97 gm (return \(local_score\);)show 340 97 gm (})show 360 233 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn (Fig)show 1 fs bu fc 2 F /|______Times-Bold fnt bn (.)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (4)show 1 fs bu fc 2 F /|______Times-Bold fnt bn ( Core algorithm: master)show 378 77 gm 0 gr 378 525 lin 397 79 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.75927 0. 32 0.07592 0.(Creating and terminating an active tuple for each task is an expensive activity in Network Linda,)awidthshow 408 79 gm 1.31683 0. 32 0.13168 0.(thus we have defined a general worker structure that can survive the end of a task and can be)awidthshow 419 79 gm (specialized when it is necessary.)show 426 78 gm (nc 422 79 434 525 6 rc)kp 0 gr 426 525 lin 455 97 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 10 fz bu fc 2 F /|______Courier fnt bn (int\312worker\(int depth\))show 467 97 gm ({)show 479 97 gm (position *root,*successor,*tree_pointer;)show 491 97 gm (int nmoves,subtree,score,value,job_type,quit,s;)show 503 97 gm (quit=false;)show 515 97 gm (while\(!quit\))show 527 115 gm ({)show 539 115 gm (in\("job",?job_type\);)show 551 115 gm (switch\312\(job_type\))show 563 133 gm ({)show 575 133 gm (case\312QUIT: /* terminate */)show 587 151 gm (quit=true;)show 599 151 gm (break;)show 611 133 gm (case\312NEW_POSITION: /* new game tree */)show 623 151 gm (in\("position",?*root\);)show 635 151 gm (in\("sync",?s\);)show 647 151 gm (out\("sync",s-1\);)show 659 151 gm (nmoves=genmoves\(root,&successor\);)show 671 151 gm (break;)show 683 133 gm (default: /* sequential )show bu fc 2 F /|______Symbol fnt bn (ab)show bu fc 2 F /|______Courier fnt bn ( */)show 695 151 gm (subtree=job_type;)show 707 151 gm (tree_pointer=successor+subtree-1;)show 719 151 gm (makemove\(tree_pointer\);)show 731 151 gm (rd\("score",?score\); /* update local score */)show 743 151 gm (value=-alphabeta\(tree_pointer,-INFINITE,-score,depth\);)show F T cp %%Page: ? 9 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 336 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Helvetica fnt bn (A Comparison of Parallel Search Algorithms)show 773 79 gm (UBLCS-94-14)show 773 519 gm (7)show 119 151 gm bu fc 2 F /|______Courier fnt bn (out\("result",value,subtree\);)show 131 151 gm (undomove\(tree_pointer\);)show 143 151 gm (break;)show 155 133 gm (})show 167 115 gm (})show 179 97 gm (return\312\(0\);})show 199 232 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn (Fig)show 1 fs bu fc 2 F /|______Times-Bold fnt bn (.)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (5)show 1 fs bu fc 2 F /|______Times-Bold fnt bn ( Core algorithm: worker)show 217 77 gm 0 gr 217 525 lin 236 79 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn 1.33102 0. 32 0.13310 0.(Our goal is to compare some parallel search strategies with their sequential versions. We have)awidthshow 247 79 gm 1.65176 0. 32 0.16517 0.(developed and tested different programs all based on such an algorithm. The experiments we)awidthshow 258 79 gm 1.15219 0. 32 0.11521 0.(describe used the Bratko)awidthshow 258 193 gm 1.17324 0. 32 0.11732 0.(-Kopec positions [BraKop82] to measure the speedup on an increasing)awidthshow 269 79 gm (number of workstations.)show 280 79 gm 0.13885 0. 32 0.01388 0.(The most important value we measured is time T to search a game tree. For sequential versions, this)awidthshow 295 79 gm 0.11901 0. 32 0.01190 0.(is defined as the interval between the root invocation of )awidthshow 295 328 gm bu fc 2 F /|______Symbol fnt bn 0.03961 0.(ab)ashow bu fc 2 F /|______Times-Roman fnt bn 0.11077 0. 32 0.01107 0.( and its termination \(we actually measure)awidthshow 307 79 gm 0.33569 0. 32 0.03356 0.(CPU time used for such an evaluation\). For the parallel versions, we let the master to measure time)awidthshow 318 79 gm 1.42822 0. 32 0.14282 0.(between the distribution of the root node and the collection of its minimax value \(for such an)awidthshow 329 79 gm 0.63201 0. 32 0.06320 0.(evaluation we used real time; the network was used during unloaded hours\). Other parameters we)awidthshow 340 79 gm (recorded are shown in Fig.6.)show 369 110 gm 1 fs 10 fz bu fc 2 F /|______Times-Bold fnt bn (Procs)show 369 167 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn (processors used for the search \(master+workers\))show 355 80 gm 0 gr 355 82 lin 355 80 gm 357 80 lin 357 82 gm 357 82 lin 357 82 lin 355 83 gm 355 161 lin 357 83 gm 357 161 lin 355 162 gm 355 164 lin 357 162 gm 357 164 lin 355 165 gm 355 468 lin 357 165 gm 357 468 lin 355 469 gm 355 471 lin 357 471 lin 357 469 gm 357 469 lin 357 469 lin 358 80 gm 371 80 lin 358 82 gm 371 82 lin 358 162 gm 371 162 lin 358 469 gm 371 469 lin 358 471 gm 371 471 lin 390 119 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (T)show 386 167 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn (total search time in seconds for all 24 positions)show 372 82 gm 0 gr 374 82 lin 372 80 gm 374 80 lin 372 83 gm 372 161 lin 374 83 gm 374 161 lin 372 162 gm 372 164 lin 374 162 gm 374 164 lin 372 165 gm 372 468 lin 374 165 gm 374 468 lin 372 471 gm 374 471 lin 372 469 gm 374 469 lin 375 80 gm 392 80 lin 375 82 gm 392 82 lin 375 162 gm 392 162 lin 375 469 gm 392 469 lin 375 471 gm 392 471 lin 411 119 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (N)show 407 167 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn (total searched nodes for all 24 positions)show 393 82 gm 0 gr 395 82 lin 393 80 gm 395 80 lin 393 83 gm 393 161 lin 395 83 gm 395 161 lin 393 162 gm 393 164 lin 395 162 gm 395 164 lin 393 165 gm 393 468 lin 395 165 gm 395 468 lin 393 471 gm 395 471 lin 393 469 gm 395 469 lin 396 80 gm 413 80 lin 396 82 gm 413 82 lin 396 162 gm 413 162 lin 396 469 gm 413 469 lin 396 471 gm 413 471 lin 437 119 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (S)show 434 167 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn (speedup )show 0 0 pen 445 254 gm (nc 419 202 445 254 6 rc)kp 0 gr 445 254 lin psb currentpoint pse 419 202 gm 419 202 lin psb 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1664 div 832 3 -1 roll exch div scale currentpoint translate 64 46 translate -23 434 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Helvetica f1 (\() show 99 434 moveto 320 /Symbol f1 (=) show 760 233 moveto 320 /Helvetica f1 (T) show 955 233 moveto 256 /Helvetica f1 (1) show 392 679 moveto 320 /Helvetica f1 (T) show 587 679 moveto 256 ns (nr) show 821 679 moveto 256 /Helvetica f1 (.) show 920 679 moveto 256 /Helvetica f1 (proc) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 366 351 moveto 1077 0 rlineto stroke 1463 434 moveto 320 /Helvetica f1 (\)) show end pse 1 1 pen 414 82 gm (nc 30 28 811 566 6 rc)kp 416 82 lin 414 80 gm 416 80 lin 414 83 gm 414 161 lin 416 83 gm 416 161 lin 414 162 gm 414 164 lin 416 162 gm 416 164 lin 414 165 gm 414 468 lin 416 165 gm 416 468 lin 414 471 gm 416 471 lin 414 469 gm 416 469 lin 417 80 gm 445 80 lin 417 82 gm 445 82 lin 417 162 gm 445 162 lin 417 469 gm 445 469 lin 417 471 gm 445 471 lin 469 119 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (E)show 466 167 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn (relative efficiency )show 0 0 pen 477 295 gm (nc 451 244 477 295 6 rc)kp 0 gr 477 295 lin psb currentpoint pse 451 244 gm 451 244 lin psb 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1632 div 832 3 -1 roll exch div scale currentpoint translate 64 42 translate -23 438 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Helvetica f1 (\() show 99 438 moveto 320 /Symbol f1 (=) show 783 237 moveto 320 /Helvetica f1 (S) show 376 683 moveto (nr) show 660 683 moveto 320 /Helvetica f1 (.) show 768 683 moveto 320 /Helvetica f1 (proc) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 366 355 moveto 1046 0 rlineto stroke 1432 438 moveto 320 /Helvetica f1 (\)) show end pse 1 1 pen 446 82 gm (nc 30 28 811 566 6 rc)kp 448 82 lin 446 80 gm 448 80 lin 446 83 gm 446 161 lin 448 83 gm 448 161 lin 446 162 gm 446 164 lin 448 162 gm 448 164 lin 446 165 gm 446 468 lin 448 165 gm 448 468 lin 446 471 gm 448 471 lin 446 469 gm 448 469 lin 449 80 gm 477 80 lin 449 82 gm 477 82 lin 449 162 gm 477 162 lin 449 469 gm 477 469 lin 449 471 gm 477 471 lin 492 112 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (Fpm)show 492 167 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn (average production factor)show 478 82 gm 0 gr 480 82 lin 478 80 gm 480 80 lin 478 83 gm 478 161 lin 480 83 gm 480 161 lin 478 162 gm 478 164 lin 480 162 gm 480 164 lin 478 165 gm 478 468 lin 480 165 gm 480 468 lin 478 471 gm 480 471 lin 478 469 gm 480 469 lin 481 80 gm 494 80 lin 481 82 gm 494 82 lin 481 162 gm 494 162 lin 481 469 gm 494 469 lin 481 471 gm 494 471 lin 509 109 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (Fpmw)show 509 167 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn (average production factor for workers)show 495 82 gm 0 gr 497 82 lin 495 80 gm 497 80 lin 495 83 gm 495 161 lin 497 83 gm 497 161 lin 495 162 gm 495 164 lin 497 162 gm 497 164 lin 495 165 gm 495 468 lin 497 165 gm 497 468 lin 495 471 gm 497 471 lin 495 469 gm 497 469 lin 498 80 gm 511 80 lin 498 82 gm 511 82 lin 498 162 gm 511 162 lin 498 469 gm 511 469 lin 498 471 gm 511 471 lin 535 116 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (SO)show 532 167 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn (search overhead )show 0 0 pen 541 299 gm (nc 517 234 541 299 6 rc)kp 0 gr 541 299 lin psb currentpoint pse 517 234 gm 517 234 lin psb 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2080 div 768 3 -1 roll exch div scale currentpoint translate 64 46 translate -23 434 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Helvetica f1 (\() show 99 434 moveto 320 /Symbol f1 (=) show 374 233 moveto 320 /Helvetica f1 (N) show 605 233 moveto 256 ns (nr) show 839 233 moveto 256 /Helvetica f1 (.) show 938 233 moveto 256 /Helvetica f1 (proc) show 751 679 moveto 320 ns (N) show 963 679 moveto 256 /Helvetica f1 (1) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 366 351 moveto 1095 0 rlineto stroke 1538 434 moveto 320 /Symbol f1 (-) show 1757 434 moveto 320 /Helvetica f1 (1) show 1888 434 moveto 320 /Helvetica f1 (\)) show end pse 1 1 pen 512 82 gm (nc 30 28 811 566 6 rc)kp 514 82 lin 512 80 gm 514 80 lin 512 83 gm 512 161 lin 514 83 gm 514 161 lin 512 162 gm 512 164 lin 514 162 gm 514 164 lin 512 165 gm 512 468 lin 514 165 gm 514 468 lin 512 471 gm 514 471 lin 512 469 gm 514 469 lin 515 80 gm 541 80 lin 515 82 gm 541 82 lin 515 162 gm 541 162 lin 515 469 gm 541 469 lin 515 471 gm 541 471 lin 565 117 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (SS)show 562 167 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn (search speed )show 0 0 pen 571 246 gm (nc 547 220 571 246 6 rc)kp 0 gr 571 246 lin psb currentpoint pse 547 220 gm 547 220 lin psb 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 832 div 768 3 -1 roll exch div scale currentpoint translate 64 46 translate -23 434 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Helvetica f1 (\() show 99 434 moveto 320 /Symbol f1 (=) show 374 233 moveto 320 /Helvetica f1 (N) show 392 679 moveto (T) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 366 351 moveto 247 0 rlineto stroke 633 434 moveto 320 /Helvetica f1 (\)) show end pse 1 1 pen 542 82 gm (nc 30 28 811 566 6 rc)kp 544 82 lin 542 80 gm 544 80 lin 542 83 gm 542 161 lin 544 83 gm 544 161 lin 542 162 gm 542 164 lin 544 162 gm 544 164 lin 542 165 gm 542 468 lin 544 165 gm 544 468 lin 542 471 gm 544 471 lin 542 469 gm 544 469 lin 545 80 gm 571 80 lin 545 82 gm 571 82 lin 545 162 gm 571 162 lin 545 469 gm 571 469 lin 545 471 gm 571 471 lin 595 114 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (S)show 9 fz bu fc 2 F /|______Times-Bold fnt bn (SS)show 592 167 gm 0 fs 10 fz bu fc 2 F /|______Times-Roman fnt bn (speed gain )show 0 0 pen 601 271 gm (nc 577 211 601 271 6 rc)kp 0 gr 601 271 lin psb currentpoint pse 577 211 gm 577 211 lin psb 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1920 div 768 3 -1 roll exch div scale currentpoint translate 64 46 translate -23 434 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Helvetica f1 (\() show 99 434 moveto 320 /Symbol f1 (=) show 389 233 moveto 320 /Helvetica f1 (VR) show 866 233 moveto 256 ns (nr) show 1100 233 moveto 256 /Helvetica f1 (.) show 1199 233 moveto 256 /Helvetica f1 (proc) show 778 679 moveto 320 ns (VR) show 1214 679 moveto 256 /Helvetica f1 (1) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 366 351 moveto 1356 0 rlineto stroke 1742 434 moveto 320 /Helvetica f1 (\)) show end pse 1 1 pen 572 82 gm (nc 30 28 811 566 6 rc)kp 574 82 lin 572 80 gm 574 80 lin 572 83 gm 572 161 lin 574 83 gm 574 161 lin 572 162 gm 572 164 lin 574 162 gm 574 164 lin 572 165 gm 572 468 lin 574 165 gm 574 468 lin 572 471 gm 574 471 lin 572 469 gm 574 469 lin 575 80 gm 601 80 lin 575 82 gm 601 82 lin 604 80 gm 604 82 lin 602 80 gm 604 80 lin 602 82 gm 602 82 lin 602 82 lin 602 83 gm 602 161 lin 604 83 gm 604 161 lin 575 162 gm 601 162 lin 602 162 gm 602 164 lin 604 162 gm 604 164 lin 602 165 gm 602 468 lin 604 165 gm 604 468 lin 575 469 gm 601 469 lin 575 471 gm 601 471 lin 604 469 gm 604 471 lin 602 471 gm 604 471 lin 602 469 gm 602 469 lin 602 469 lin 616 79 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (Fig 6)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( )show 2 fs bu fc 2 F /|______Times-Italic fnt bn (Parameters we measured in the experiments)show 632 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.66162 0. 32 0.06616 0.(All experiments were done fixing a search depth of 5 plies, for comparison with other papers that)awidthshow 643 79 gm 0.46813 0. 32 0.04681 0.(used the same search depth. We have used 11 Sun Sparcstations in periods when they were free of)awidthshow 654 79 gm (other tasks.)show 684 79 gm 1 fs 12 fz bu fc 2 F /|______Times-Bold fnt bn (4. Static splitting)show 697 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.44723 0. 32 0.04472 0.(Let us discuss preliminarly a few results we can expect from our experiments. Let B the branching)awidthshow 708 79 gm (factor typical of chess game trees, and N)show 9 fz bu fc 2 F /|______Times-Roman fnt bn (w )show 11 fz bu fc 2 F /|______Times-Roman fnt bn (the number of processors available for explorers:)show 720 88 gm (\245\312the core algorithm efficiency should be proportional to the ratio B/N)show 720 396 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (w)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( [MarCam82];)show 737 88 gm 0.22293 0. 32 0.02229 0.(\245\312for a game tree with B=40, an )awidthshow bu fc 2 F /|______Symbol fnt bn 0.10455 0.(ab)ashow bu fc 2 F /|______Times-Roman fnt bn 0.24337 0. 32 0.02433 0.( search is equivalent to a minimax search of a tree with branch)awidthshow 749 101 gm (factor B=7 [Gil72]. Thus, if we had N)show 9 fz bu fc 2 F /|______Times-Roman fnt bn (w)show 11 fz bu fc 2 F /|______Times-Roman fnt bn (=40 explorers, the ideal average speedup should be 7.)show F T cp %%Page: ? 10 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 336 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Helvetica fnt bn (A Comparison of Parallel Search Algorithms)show 773 79 gm (UBLCS-94-14)show 773 519 gm (8)show 136 96 gm 1 fs 9 fz bu fc 2 F /|______Times-Bold fnt bn (Procs)show 136 141 gm 10 fz bu fc 2 F /|______Times-Bold fnt bn (T\(sec\))show 136 188 gm 9 fz bu fc 2 F /|______Times-Bold fnt bn (N \(nodes\))show 136 249 gm 10 fz bu fc 2 F /|______Times-Bold fnt bn (S)show 136 282 gm (E)show 136 310 gm (Fpm)show 136 344 gm 9 fz bu fc 2 F /|______Times-Bold fnt bn (Fpmw)show 136 385 gm 10 fz bu fc 2 F /|______Times-Bold fnt bn (SO)show 136 425 gm 9 fz bu fc 2 F /|______Times-Bold fnt bn (SS \(nodes/sec\))show 136 505 gm 10 fz bu fc 2 F /|______Times-Bold fnt bn (Sss)show 122 80 gm 0 gr 122 82 lin 122 80 gm 124 80 lin 124 82 gm 124 82 lin 124 82 lin 122 83 gm 122 128 lin 124 83 gm 124 128 lin 122 129 gm 122 131 lin 124 129 gm 124 131 lin 122 132 gm 122 175 lin 124 132 gm 124 175 lin 122 176 gm 122 178 lin 124 176 gm 124 178 lin 122 179 gm 122 232 lin 124 179 gm 124 232 lin 122 233 gm 122 235 lin 124 233 gm 124 235 lin 122 236 gm 122 266 lin 124 236 gm 124 266 lin 122 267 gm 122 269 lin 124 267 gm 124 269 lin 122 270 gm 122 300 lin 124 270 gm 124 300 lin 122 301 gm 122 303 lin 124 301 gm 124 303 lin 122 304 gm 122 334 lin 124 304 gm 124 334 lin 122 335 gm 122 337 lin 124 335 gm 124 337 lin 122 338 gm 122 372 lin 124 338 gm 124 372 lin 122 373 gm 122 375 lin 124 373 gm 124 375 lin 122 376 gm 122 406 lin 124 376 gm 124 406 lin 122 407 gm 122 409 lin 124 407 gm 124 409 lin 122 410 gm 122 492 lin 124 410 gm 124 492 lin 122 493 gm 122 495 lin 124 493 gm 124 495 lin 122 496 gm 122 526 lin 124 496 gm 124 526 lin 122 527 gm 122 529 lin 124 529 lin 124 527 gm 124 527 lin 124 527 lin 125 80 gm 138 80 lin 125 82 gm 138 82 lin 125 129 gm 138 129 lin 125 131 gm 138 131 lin 125 176 gm 138 176 lin 125 178 gm 138 178 lin 125 233 gm 138 233 lin 125 235 gm 138 235 lin 125 267 gm 138 267 lin 125 269 gm 138 269 lin 125 301 gm 138 301 lin 125 303 gm 138 303 lin 125 335 gm 138 335 lin 125 337 gm 138 337 lin 125 373 gm 138 373 lin 125 375 gm 138 375 lin 125 407 gm 138 407 lin 125 409 gm 138 409 lin 125 493 gm 138 493 lin 125 495 gm 138 495 lin 125 527 gm 138 527 lin 125 529 gm 138 529 lin 153 104 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn (1)show 153 144 gm (8301)show 153 189 gm (5347545)show 153 247 gm (---)show 153 281 gm (---)show 153 315 gm (---)show 153 351 gm (---)show 153 387 gm (---)show 153 444 gm (644)show 153 507 gm (---)show 139 82 gm 0 gr 141 82 lin 139 80 gm 141 80 lin 139 83 gm 139 128 lin 141 83 gm 141 128 lin 139 131 gm 139 131 lin 141 129 gm 141 129 lin 139 129 gm 139 129 lin 141 131 gm 141 131 lin 139 132 gm 139 175 lin 141 132 gm 141 175 lin 139 178 gm 139 178 lin 141 176 gm 141 176 lin 139 176 gm 139 176 lin 141 178 gm 141 178 lin 139 179 gm 139 232 lin 141 179 gm 141 232 lin 139 235 gm 139 235 lin 141 233 gm 141 233 lin 139 233 gm 139 233 lin 141 235 gm 141 235 lin 139 236 gm 139 266 lin 141 236 gm 141 266 lin 139 269 gm 139 269 lin 141 267 gm 141 267 lin 139 267 gm 139 267 lin 141 269 gm 141 269 lin 139 270 gm 139 300 lin 141 270 gm 141 300 lin 139 303 gm 139 303 lin 141 301 gm 141 301 lin 139 301 gm 139 301 lin 141 303 gm 141 303 lin 139 304 gm 139 334 lin 141 304 gm 141 334 lin 139 337 gm 139 337 lin 141 335 gm 141 335 lin 139 335 gm 139 335 lin 141 337 gm 141 337 lin 139 338 gm 139 372 lin 141 338 gm 141 372 lin 139 375 gm 139 375 lin 141 373 gm 141 373 lin 139 373 gm 139 373 lin 141 375 gm 141 375 lin 139 376 gm 139 406 lin 141 376 gm 141 406 lin 139 409 gm 139 409 lin 141 407 gm 141 407 lin 139 407 gm 139 407 lin 141 409 gm 141 409 lin 139 410 gm 139 492 lin 141 410 gm 141 492 lin 139 495 gm 139 495 lin 141 493 gm 141 493 lin 139 493 gm 139 493 lin 141 495 gm 141 495 lin 139 496 gm 139 526 lin 141 496 gm 141 526 lin 139 529 gm 141 529 lin 139 527 gm 141 527 lin 142 80 gm 155 80 lin 142 82 gm 155 82 lin 142 129 gm 155 129 lin 142 131 gm 155 131 lin 142 176 gm 155 176 lin 142 178 gm 155 178 lin 142 233 gm 155 233 lin 142 235 gm 155 235 lin 142 267 gm 155 267 lin 142 269 gm 155 269 lin 142 301 gm 155 301 lin 142 303 gm 155 303 lin 142 335 gm 155 335 lin 142 337 gm 155 337 lin 142 373 gm 155 373 lin 142 375 gm 155 375 lin 142 407 gm 155 407 lin 142 409 gm 155 409 lin 142 493 gm 155 493 lin 142 495 gm 155 495 lin 142 527 gm 155 527 lin 142 529 gm 155 529 lin 168 104 gm F 1 setTxMode (3)show 168 144 gm (4571)show 168 189 gm (5754203)show 168 243 gm (1.82)show 168 277 gm (0.61)show 168 311 gm (0.66)show 168 347 gm (0.98)show 168 383 gm (0.08)show 168 442 gm (1259)show 168 503 gm (1.95)show 156 82 gm 0 gr 156 82 lin 156 80 gm 156 80 lin 156 83 gm 156 128 lin 156 131 gm 156 131 lin 156 129 gm 156 129 lin 156 132 gm 156 175 lin 156 178 gm 156 178 lin 156 176 gm 156 176 lin 156 179 gm 156 232 lin 156 235 gm 156 235 lin 156 233 gm 156 233 lin 156 236 gm 156 266 lin 156 269 gm 156 269 lin 156 267 gm 156 267 lin 156 270 gm 156 300 lin 156 303 gm 156 303 lin 156 301 gm 156 301 lin 156 304 gm 156 334 lin 156 337 gm 156 337 lin 156 335 gm 156 335 lin 156 338 gm 156 372 lin 156 375 gm 156 375 lin 156 373 gm 156 373 lin 156 376 gm 156 406 lin 156 409 gm 156 409 lin 156 407 gm 156 407 lin 156 410 gm 156 492 lin 156 495 gm 156 495 lin 156 493 gm 156 493 lin 156 496 gm 156 526 lin 156 529 gm 156 529 lin 156 527 gm 156 527 lin 157 80 gm 170 80 lin 157 82 gm 170 82 lin 157 129 gm 170 129 lin 157 131 gm 170 131 lin 157 176 gm 170 176 lin 157 178 gm 170 178 lin 157 233 gm 170 233 lin 157 235 gm 170 235 lin 157 267 gm 170 267 lin 157 269 gm 170 269 lin 157 301 gm 170 301 lin 157 303 gm 170 303 lin 157 335 gm 170 335 lin 157 337 gm 170 337 lin 157 373 gm 170 373 lin 157 375 gm 170 375 lin 157 407 gm 170 407 lin 157 409 gm 170 409 lin 157 493 gm 170 493 lin 157 495 gm 170 495 lin 157 527 gm 170 527 lin 157 529 gm 170 529 lin 183 104 gm F 1 setTxMode (5)show 183 144 gm (2770)show 183 189 gm (6599460)show 183 243 gm (3.00)show 183 277 gm (0.60)show 183 311 gm (0.75)show 183 347 gm (0.93)show 183 383 gm (0.23)show 183 442 gm (2382)show 183 503 gm (3.70)show 171 82 gm 0 gr 171 82 lin 171 80 gm 171 80 lin 171 83 gm 171 128 lin 171 131 gm 171 131 lin 171 129 gm 171 129 lin 171 132 gm 171 175 lin 171 178 gm 171 178 lin 171 176 gm 171 176 lin 171 179 gm 171 232 lin 171 235 gm 171 235 lin 171 233 gm 171 233 lin 171 236 gm 171 266 lin 171 269 gm 171 269 lin 171 267 gm 171 267 lin 171 270 gm 171 300 lin 171 303 gm 171 303 lin 171 301 gm 171 301 lin 171 304 gm 171 334 lin 171 337 gm 171 337 lin 171 335 gm 171 335 lin 171 338 gm 171 372 lin 171 375 gm 171 375 lin 171 373 gm 171 373 lin 171 376 gm 171 406 lin 171 409 gm 171 409 lin 171 407 gm 171 407 lin 171 410 gm 171 492 lin 171 495 gm 171 495 lin 171 493 gm 171 493 lin 171 496 gm 171 526 lin 171 529 gm 171 529 lin 171 527 gm 171 527 lin 172 80 gm 185 80 lin 172 82 gm 185 82 lin 172 129 gm 185 129 lin 172 131 gm 185 131 lin 172 176 gm 185 176 lin 172 178 gm 185 178 lin 172 233 gm 185 233 lin 172 235 gm 185 235 lin 172 267 gm 185 267 lin 172 269 gm 185 269 lin 172 301 gm 185 301 lin 172 303 gm 185 303 lin 172 335 gm 185 335 lin 172 337 gm 185 337 lin 172 373 gm 185 373 lin 172 375 gm 185 375 lin 172 407 gm 185 407 lin 172 409 gm 185 409 lin 172 493 gm 185 493 lin 172 495 gm 185 495 lin 172 527 gm 185 527 lin 172 529 gm 185 529 lin 198 104 gm F 1 setTxMode (7)show 198 144 gm (2242)show 198 189 gm (7236560)show 198 243 gm (3.70)show 198 277 gm (0.53)show 198 311 gm (0.71)show 198 347 gm (0.83)show 198 383 gm (0.35)show 198 442 gm (3228)show 198 503 gm (5.01)show 186 82 gm 0 gr 186 82 lin 186 80 gm 186 80 lin 186 83 gm 186 128 lin 186 131 gm 186 131 lin 186 129 gm 186 129 lin 186 132 gm 186 175 lin 186 178 gm 186 178 lin 186 176 gm 186 176 lin 186 179 gm 186 232 lin 186 235 gm 186 235 lin 186 233 gm 186 233 lin 186 236 gm 186 266 lin 186 269 gm 186 269 lin 186 267 gm 186 267 lin 186 270 gm 186 300 lin 186 303 gm 186 303 lin 186 301 gm 186 301 lin 186 304 gm 186 334 lin 186 337 gm 186 337 lin 186 335 gm 186 335 lin 186 338 gm 186 372 lin 186 375 gm 186 375 lin 186 373 gm 186 373 lin 186 376 gm 186 406 lin 186 409 gm 186 409 lin 186 407 gm 186 407 lin 186 410 gm 186 492 lin 186 495 gm 186 495 lin 186 493 gm 186 493 lin 186 496 gm 186 526 lin 186 529 gm 186 529 lin 186 527 gm 186 527 lin 187 80 gm 200 80 lin 187 82 gm 200 82 lin 187 129 gm 200 129 lin 187 131 gm 200 131 lin 187 176 gm 200 176 lin 187 178 gm 200 178 lin 187 233 gm 200 233 lin 187 235 gm 200 235 lin 187 267 gm 200 267 lin 187 269 gm 200 269 lin 187 301 gm 200 301 lin 187 303 gm 200 303 lin 187 335 gm 200 335 lin 187 337 gm 200 337 lin 187 373 gm 200 373 lin 187 375 gm 200 375 lin 187 407 gm 200 407 lin 187 409 gm 200 409 lin 187 493 gm 200 493 lin 187 495 gm 200 495 lin 187 527 gm 200 527 lin 187 529 gm 200 529 lin 213 104 gm F 1 setTxMode (9)show 213 144 gm (1988)show 213 189 gm (7876769)show 213 243 gm (4.18)show 213 277 gm (0.46)show 213 311 gm (0.68)show 213 347 gm (0.77)show 213 383 gm (0.47)show 213 442 gm (3962)show 213 503 gm (6.15)show 201 82 gm 0 gr 201 82 lin 201 80 gm 201 80 lin 201 83 gm 201 128 lin 201 131 gm 201 131 lin 201 129 gm 201 129 lin 201 132 gm 201 175 lin 201 178 gm 201 178 lin 201 176 gm 201 176 lin 201 179 gm 201 232 lin 201 235 gm 201 235 lin 201 233 gm 201 233 lin 201 236 gm 201 266 lin 201 269 gm 201 269 lin 201 267 gm 201 267 lin 201 270 gm 201 300 lin 201 303 gm 201 303 lin 201 301 gm 201 301 lin 201 304 gm 201 334 lin 201 337 gm 201 337 lin 201 335 gm 201 335 lin 201 338 gm 201 372 lin 201 375 gm 201 375 lin 201 373 gm 201 373 lin 201 376 gm 201 406 lin 201 409 gm 201 409 lin 201 407 gm 201 407 lin 201 410 gm 201 492 lin 201 495 gm 201 495 lin 201 493 gm 201 493 lin 201 496 gm 201 526 lin 201 529 gm 201 529 lin 201 527 gm 201 527 lin 202 80 gm 215 80 lin 202 82 gm 215 82 lin 202 129 gm 215 129 lin 202 131 gm 215 131 lin 202 176 gm 215 176 lin 202 178 gm 215 178 lin 202 233 gm 215 233 lin 202 235 gm 215 235 lin 202 267 gm 215 267 lin 202 269 gm 215 269 lin 202 301 gm 215 301 lin 202 303 gm 215 303 lin 202 335 gm 215 335 lin 202 337 gm 215 337 lin 202 373 gm 215 373 lin 202 375 gm 215 375 lin 202 407 gm 215 407 lin 202 409 gm 215 409 lin 202 493 gm 215 493 lin 202 495 gm 215 495 lin 202 527 gm 215 527 lin 202 529 gm 215 529 lin 228 101 gm F 1 setTxMode (11)show 228 144 gm (1786)show 228 189 gm (8521288)show 228 243 gm (4.65)show 228 277 gm (0.42)show 228 311 gm (0.66)show 228 347 gm (0.73)show 228 383 gm (0.59)show 228 442 gm (4771)show 228 503 gm (7.41)show 216 82 gm 0 gr 216 82 lin 216 80 gm 216 80 lin 216 83 gm 216 128 lin 216 131 gm 216 131 lin 216 129 gm 216 129 lin 216 132 gm 216 175 lin 216 178 gm 216 178 lin 216 176 gm 216 176 lin 216 179 gm 216 232 lin 216 235 gm 216 235 lin 216 233 gm 216 233 lin 216 236 gm 216 266 lin 216 269 gm 216 269 lin 216 267 gm 216 267 lin 216 270 gm 216 300 lin 216 303 gm 216 303 lin 216 301 gm 216 301 lin 216 304 gm 216 334 lin 216 337 gm 216 337 lin 216 335 gm 216 335 lin 216 338 gm 216 372 lin 216 375 gm 216 375 lin 216 373 gm 216 373 lin 216 376 gm 216 406 lin 216 409 gm 216 409 lin 216 407 gm 216 407 lin 216 410 gm 216 492 lin 216 495 gm 216 495 lin 216 493 gm 216 493 lin 216 496 gm 216 526 lin 216 529 gm 216 529 lin 216 527 gm 216 527 lin 217 80 gm 230 80 lin 217 82 gm 230 82 lin 233 80 gm 233 82 lin 231 80 gm 233 80 lin 231 82 gm 231 82 lin 231 82 lin 231 83 gm 231 128 lin 233 83 gm 233 128 lin 217 129 gm 230 129 lin 217 131 gm 230 131 lin 231 129 gm 231 131 lin 233 129 gm 233 131 lin 231 132 gm 231 175 lin 233 132 gm 233 175 lin 217 176 gm 230 176 lin 217 178 gm 230 178 lin 231 176 gm 231 178 lin 233 176 gm 233 178 lin 231 179 gm 231 232 lin 233 179 gm 233 232 lin 217 233 gm 230 233 lin 217 235 gm 230 235 lin 231 233 gm 231 235 lin 233 233 gm 233 235 lin 231 236 gm 231 266 lin 233 236 gm 233 266 lin 217 267 gm 230 267 lin 217 269 gm 230 269 lin 231 267 gm 231 269 lin 233 267 gm 233 269 lin 231 270 gm 231 300 lin 233 270 gm 233 300 lin 217 301 gm 230 301 lin 217 303 gm 230 303 lin 231 301 gm 231 303 lin 233 301 gm 233 303 lin 231 304 gm 231 334 lin 233 304 gm 233 334 lin 217 335 gm 230 335 lin 217 337 gm 230 337 lin 231 335 gm 231 337 lin 233 335 gm 233 337 lin 231 338 gm 231 372 lin 233 338 gm 233 372 lin 217 373 gm 230 373 lin 217 375 gm 230 375 lin 231 373 gm 231 375 lin 233 373 gm 233 375 lin 231 376 gm 231 406 lin 233 376 gm 233 406 lin 217 407 gm 230 407 lin 217 409 gm 230 409 lin 231 407 gm 231 409 lin 233 407 gm 233 409 lin 231 410 gm 231 492 lin 233 410 gm 233 492 lin 217 493 gm 230 493 lin 217 495 gm 230 495 lin 231 493 gm 231 495 lin 233 493 gm 233 495 lin 231 496 gm 231 526 lin 233 496 gm 233 526 lin 217 527 gm 230 527 lin 217 529 gm 230 529 lin 233 527 gm 233 529 lin 231 529 gm 233 529 lin 231 527 gm 231 527 lin 231 527 lin 245 79 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (Fig. 7)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( )show 2 fs bu fc 2 F /|______Times-Italic fnt bn (Results of experiments for core algorithm)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( \(basic master worker\))show 261 79 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.32440 0. 32 0.03244 0.(In Fig. 7 we show data for the core algorithm. The reported speedup is low; moreover, values for E)awidthshow 272 79 gm (tell that adding processors we increase all overheads:)show 284 88 gm 2.20611 0. 32 0.22061 0.(\245\312search overhead: compare real speedup S with ideal speedup S)awidthshow 284 403 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.49050 0.(ss)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 2.22335 0. 32 0.22233 0.(. For instance, with 11)awidthshow 295 101 gm 2.43774 0. 32 0.24377 0.(processors we have a 37% loss \(S)awidthshow 295 271 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.33930 0.(ss)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 2.01950 0. 32 0.20195 0.(=7.41\312vs\312S=4.65\). This loss is caused by minimum)awidthshow 306 101 gm 0.54733 0. 32 0.05473 0.(cooperation. We also remark that search overhead increases with more processors because all)awidthshow 317 101 gm 0.40542 0. 32 0.04054 0.(workers start with value = -)awidthshow currentfont SwToSym 0.40542 0. 32 0.04054 0.(\245)awidthshow setfont 0.40542 0. 32 0.04054 0.( , whereas the sequential search has a good approximation of the)awidthshow 328 101 gm (value starting from the second subtree.)show 341 88 gm 1.70776 0. 32 0.17077 0.(\245\312communication and synchronization overhead: F)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.38545 0.(pm)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 1.18698 0. 32 0.11869 0.( increases until 5 processors \(75%\) then)awidthshow 352 101 gm 0.20828 0. 32 0.02082 0.(decreases; for 11 processors the F)awidthshow 352 251 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.07923 0.(pm)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.21224 0. 32 0.02122 0.( value is almost the same as with 3 processors \(66%\). This)awidthshow 363 101 gm 0.66604 0. 32 0.06660 0.(is explained by the fact that the master is idle most of the time, so if we use one process per)awidthshow 374 101 gm (processor a processor is idle as well.)show 404 96 gm 1 fs 10 fz bu fc 2 F /|______Times-Bold fnt bn (Procs)show 404 145 gm (T\312\(sec\))show 404 200 gm (N\312\(nodes\))show 404 271 gm (S)show 404 308 gm (E)show 404 338 gm (Fpm)show 404 378 gm (SO)show 404 416 gm (SS\312\(nodes/sec\))show 404 502 gm (Sss)show 390 80 gm 0 gr 390 82 lin 390 80 gm 392 80 lin 392 82 gm 392 82 lin 392 82 lin 390 83 gm 390 131 lin 392 83 gm 392 131 lin 390 132 gm 390 134 lin 392 132 gm 392 134 lin 390 135 gm 390 182 lin 392 135 gm 392 182 lin 390 183 gm 390 185 lin 392 183 gm 392 185 lin 390 186 gm 390 253 lin 392 186 gm 392 253 lin 390 254 gm 390 256 lin 392 254 gm 392 256 lin 390 257 gm 390 290 lin 392 257 gm 392 290 lin 390 291 gm 390 293 lin 392 291 gm 392 293 lin 390 294 gm 390 327 lin 392 294 gm 392 327 lin 390 328 gm 390 330 lin 392 328 gm 392 330 lin 390 331 gm 390 364 lin 392 331 gm 392 364 lin 390 365 gm 390 367 lin 392 365 gm 392 367 lin 390 368 gm 390 400 lin 392 368 gm 392 400 lin 390 401 gm 390 403 lin 392 401 gm 392 403 lin 390 404 gm 390 487 lin 392 404 gm 392 487 lin 390 488 gm 390 490 lin 392 488 gm 392 490 lin 390 491 gm 390 524 lin 392 491 gm 392 524 lin 390 525 gm 390 527 lin 392 527 lin 392 525 gm 392 525 lin 392 525 lin 393 80 gm 406 80 lin 393 82 gm 406 82 lin 393 132 gm 406 132 lin 393 134 gm 406 134 lin 393 183 gm 406 183 lin 393 185 gm 406 185 lin 393 254 gm 406 254 lin 393 256 gm 406 256 lin 393 291 gm 406 291 lin 393 293 gm 406 293 lin 393 328 gm 406 328 lin 393 330 gm 406 330 lin 393 365 gm 406 365 lin 393 367 gm 406 367 lin 393 401 gm 406 401 lin 393 403 gm 406 403 lin 393 488 gm 406 488 lin 393 490 gm 406 490 lin 393 525 gm 406 525 lin 393 527 gm 406 527 lin 421 105 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn (1)show 421 149 gm (8301)show 421 203 gm (5347545)show 421 269 gm (---)show 421 306 gm (---)show 421 343 gm (---)show 421 380 gm (---)show 421 439 gm (644)show 421 503 gm (---)show 407 82 gm 0 gr 409 82 lin 407 80 gm 409 80 lin 407 83 gm 407 131 lin 409 83 gm 409 131 lin 407 134 gm 407 134 lin 409 132 gm 409 132 lin 407 132 gm 407 132 lin 409 134 gm 409 134 lin 407 135 gm 407 182 lin 409 135 gm 409 182 lin 407 185 gm 407 185 lin 409 183 gm 409 183 lin 407 183 gm 407 183 lin 409 185 gm 409 185 lin 407 186 gm 407 253 lin 409 186 gm 409 253 lin 407 256 gm 407 256 lin 409 254 gm 409 254 lin 407 254 gm 407 254 lin 409 256 gm 409 256 lin 407 257 gm 407 290 lin 409 257 gm 409 290 lin 407 293 gm 407 293 lin 409 291 gm 409 291 lin 407 291 gm 407 291 lin 409 293 gm 409 293 lin 407 294 gm 407 327 lin 409 294 gm 409 327 lin 407 330 gm 407 330 lin 409 328 gm 409 328 lin 407 328 gm 407 328 lin 409 330 gm 409 330 lin 407 331 gm 407 364 lin 409 331 gm 409 364 lin 407 367 gm 407 367 lin 409 365 gm 409 365 lin 407 365 gm 407 365 lin 409 367 gm 409 367 lin 407 368 gm 407 400 lin 409 368 gm 409 400 lin 407 403 gm 407 403 lin 409 401 gm 409 401 lin 407 401 gm 407 401 lin 409 403 gm 409 403 lin 407 404 gm 407 487 lin 409 404 gm 409 487 lin 407 490 gm 407 490 lin 409 488 gm 409 488 lin 407 488 gm 407 488 lin 409 490 gm 409 490 lin 407 491 gm 407 524 lin 409 491 gm 409 524 lin 407 527 gm 409 527 lin 407 525 gm 409 525 lin 410 80 gm 423 80 lin 410 82 gm 423 82 lin 410 132 gm 423 132 lin 410 134 gm 423 134 lin 410 183 gm 423 183 lin 410 185 gm 423 185 lin 410 254 gm 423 254 lin 410 256 gm 423 256 lin 410 291 gm 423 291 lin 410 293 gm 423 293 lin 410 328 gm 423 328 lin 410 330 gm 423 330 lin 410 365 gm 423 365 lin 410 367 gm 423 367 lin 410 401 gm 423 401 lin 410 403 gm 423 403 lin 410 488 gm 423 488 lin 410 490 gm 423 490 lin 410 525 gm 423 525 lin 410 527 gm 423 527 lin 436 105 gm F 1 setTxMode (3)show 436 149 gm (4544)show 436 203 gm (5860668)show 436 265 gm (1.83)show 436 302 gm (0.61)show 436 339 gm (0.70)show 436 376 gm (0.10)show 436 436 gm (1290)show 436 499 gm (2.00)show 424 82 gm 0 gr 424 82 lin 424 80 gm 424 80 lin 424 83 gm 424 131 lin 424 134 gm 424 134 lin 424 132 gm 424 132 lin 424 135 gm 424 182 lin 424 185 gm 424 185 lin 424 183 gm 424 183 lin 424 186 gm 424 253 lin 424 256 gm 424 256 lin 424 254 gm 424 254 lin 424 257 gm 424 290 lin 424 293 gm 424 293 lin 424 291 gm 424 291 lin 424 294 gm 424 327 lin 424 330 gm 424 330 lin 424 328 gm 424 328 lin 424 331 gm 424 364 lin 424 367 gm 424 367 lin 424 365 gm 424 365 lin 424 368 gm 424 400 lin 424 403 gm 424 403 lin 424 401 gm 424 401 lin 424 404 gm 424 487 lin 424 490 gm 424 490 lin 424 488 gm 424 488 lin 424 491 gm 424 524 lin 424 527 gm 424 527 lin 424 525 gm 424 525 lin 425 80 gm 438 80 lin 425 82 gm 438 82 lin 425 132 gm 438 132 lin 425 134 gm 438 134 lin 425 183 gm 438 183 lin 425 185 gm 438 185 lin 425 254 gm 438 254 lin 425 256 gm 438 256 lin 425 291 gm 438 291 lin 425 293 gm 438 293 lin 425 328 gm 438 328 lin 425 330 gm 438 330 lin 425 365 gm 438 365 lin 425 367 gm 438 367 lin 425 401 gm 438 401 lin 425 403 gm 438 403 lin 425 488 gm 438 488 lin 425 490 gm 438 490 lin 425 525 gm 438 525 lin 425 527 gm 438 527 lin 451 105 gm F 1 setTxMode (5)show 451 149 gm (3173)show 451 203 gm (6330053)show 451 265 gm (2.62)show 451 302 gm (0.52)show 451 339 gm (0.66)show 451 376 gm (0.18)show 451 436 gm (1995)show 451 499 gm (3.10)show 439 82 gm 0 gr 439 82 lin 439 80 gm 439 80 lin 439 83 gm 439 131 lin 439 134 gm 439 134 lin 439 132 gm 439 132 lin 439 135 gm 439 182 lin 439 185 gm 439 185 lin 439 183 gm 439 183 lin 439 186 gm 439 253 lin 439 256 gm 439 256 lin 439 254 gm 439 254 lin 439 257 gm 439 290 lin 439 293 gm 439 293 lin 439 291 gm 439 291 lin 439 294 gm 439 327 lin 439 330 gm 439 330 lin 439 328 gm 439 328 lin 439 331 gm 439 364 lin 439 367 gm 439 367 lin 439 365 gm 439 365 lin 439 368 gm 439 400 lin 439 403 gm 439 403 lin 439 401 gm 439 401 lin 439 404 gm 439 487 lin 439 490 gm 439 490 lin 439 488 gm 439 488 lin 439 491 gm 439 524 lin 439 527 gm 439 527 lin 439 525 gm 439 525 lin 440 80 gm 453 80 lin 440 82 gm 453 82 lin 440 132 gm 453 132 lin 440 134 gm 453 134 lin 440 183 gm 453 183 lin 440 185 gm 453 185 lin 440 254 gm 453 254 lin 440 256 gm 453 256 lin 440 291 gm 453 291 lin 440 293 gm 453 293 lin 440 328 gm 453 328 lin 440 330 gm 453 330 lin 440 365 gm 453 365 lin 440 367 gm 453 367 lin 440 401 gm 453 401 lin 440 403 gm 453 403 lin 440 488 gm 453 488 lin 440 490 gm 453 490 lin 440 525 gm 453 525 lin 440 527 gm 453 527 lin 466 105 gm F 1 setTxMode (7)show 466 149 gm (2779)show 466 203 gm (6867688)show 466 265 gm (2.99)show 466 302 gm (0.43)show 466 339 gm (0.61)show 466 376 gm (0.28)show 466 436 gm (2471)show 466 499 gm (3.84)show 454 82 gm 0 gr 454 82 lin 454 80 gm 454 80 lin 454 83 gm 454 131 lin 454 134 gm 454 134 lin 454 132 gm 454 132 lin 454 135 gm 454 182 lin 454 185 gm 454 185 lin 454 183 gm 454 183 lin 454 186 gm 454 253 lin 454 256 gm 454 256 lin 454 254 gm 454 254 lin 454 257 gm 454 290 lin 454 293 gm 454 293 lin 454 291 gm 454 291 lin 454 294 gm 454 327 lin 454 330 gm 454 330 lin 454 328 gm 454 328 lin 454 331 gm 454 364 lin 454 367 gm 454 367 lin 454 365 gm 454 365 lin 454 368 gm 454 400 lin 454 403 gm 454 403 lin 454 401 gm 454 401 lin 454 404 gm 454 487 lin 454 490 gm 454 490 lin 454 488 gm 454 488 lin 454 491 gm 454 524 lin 454 527 gm 454 527 lin 454 525 gm 454 525 lin 455 80 gm 468 80 lin 455 82 gm 468 82 lin 455 132 gm 468 132 lin 455 134 gm 468 134 lin 455 183 gm 468 183 lin 455 185 gm 468 185 lin 455 254 gm 468 254 lin 455 256 gm 468 256 lin 455 291 gm 468 291 lin 455 293 gm 468 293 lin 455 328 gm 468 328 lin 455 330 gm 468 330 lin 455 365 gm 468 365 lin 455 367 gm 468 367 lin 455 401 gm 468 401 lin 455 403 gm 468 403 lin 455 488 gm 468 488 lin 455 490 gm 468 490 lin 455 525 gm 468 525 lin 455 527 gm 468 527 lin 481 105 gm F 1 setTxMode (9)show 481 149 gm (2517)show 481 203 gm (7310806)show 481 265 gm (3.30)show 481 302 gm (0.37)show 481 339 gm (0.57)show 481 376 gm (0.37)show 481 436 gm (2905)show 481 499 gm (4.51)show 469 82 gm 0 gr 469 82 lin 469 80 gm 469 80 lin 469 83 gm 469 131 lin 469 134 gm 469 134 lin 469 132 gm 469 132 lin 469 135 gm 469 182 lin 469 185 gm 469 185 lin 469 183 gm 469 183 lin 469 186 gm 469 253 lin 469 256 gm 469 256 lin 469 254 gm 469 254 lin 469 257 gm 469 290 lin 469 293 gm 469 293 lin 469 291 gm 469 291 lin 469 294 gm 469 327 lin 469 330 gm 469 330 lin 469 328 gm 469 328 lin 469 331 gm 469 364 lin 469 367 gm 469 367 lin 469 365 gm 469 365 lin 469 368 gm 469 400 lin 469 403 gm 469 403 lin 469 401 gm 469 401 lin 469 404 gm 469 487 lin 469 490 gm 469 490 lin 469 488 gm 469 488 lin 469 491 gm 469 524 lin 469 527 gm 469 527 lin 469 525 gm 469 525 lin 470 80 gm 483 80 lin 470 82 gm 483 82 lin 470 132 gm 483 132 lin 470 134 gm 483 134 lin 470 183 gm 483 183 lin 470 185 gm 483 185 lin 470 254 gm 483 254 lin 470 256 gm 483 256 lin 470 291 gm 483 291 lin 470 293 gm 483 293 lin 470 328 gm 483 328 lin 470 330 gm 483 330 lin 470 365 gm 483 365 lin 470 367 gm 483 367 lin 470 401 gm 483 401 lin 470 403 gm 483 403 lin 470 488 gm 483 488 lin 470 490 gm 483 490 lin 470 525 gm 483 525 lin 470 527 gm 483 527 lin 496 103 gm F 1 setTxMode (11)show 496 149 gm (2310)show 496 203 gm (7990369)show 496 265 gm (3.59)show 496 302 gm (0.33)show 496 339 gm (0.54)show 496 376 gm (0.49)show 496 436 gm (3459)show 496 499 gm (5.37)show 484 82 gm 0 gr 484 82 lin 484 80 gm 484 80 lin 484 83 gm 484 131 lin 484 134 gm 484 134 lin 484 132 gm 484 132 lin 484 135 gm 484 182 lin 484 185 gm 484 185 lin 484 183 gm 484 183 lin 484 186 gm 484 253 lin 484 256 gm 484 256 lin 484 254 gm 484 254 lin 484 257 gm 484 290 lin 484 293 gm 484 293 lin 484 291 gm 484 291 lin 484 294 gm 484 327 lin 484 330 gm 484 330 lin 484 328 gm 484 328 lin 484 331 gm 484 364 lin 484 367 gm 484 367 lin 484 365 gm 484 365 lin 484 368 gm 484 400 lin 484 403 gm 484 403 lin 484 401 gm 484 401 lin 484 404 gm 484 487 lin 484 490 gm 484 490 lin 484 488 gm 484 488 lin 484 491 gm 484 524 lin 484 527 gm 484 527 lin 484 525 gm 484 525 lin 485 80 gm 498 80 lin 485 82 gm 498 82 lin 501 80 gm 501 82 lin 499 80 gm 501 80 lin 499 82 gm 499 82 lin 499 82 lin 499 83 gm 499 131 lin 501 83 gm 501 131 lin 485 132 gm 498 132 lin 485 134 gm 498 134 lin 499 132 gm 499 134 lin 501 132 gm 501 134 lin 499 135 gm 499 182 lin 501 135 gm 501 182 lin 485 183 gm 498 183 lin 485 185 gm 498 185 lin 499 183 gm 499 185 lin 501 183 gm 501 185 lin 499 186 gm 499 253 lin 501 186 gm 501 253 lin 485 254 gm 498 254 lin 485 256 gm 498 256 lin 499 254 gm 499 256 lin 501 254 gm 501 256 lin 499 257 gm 499 290 lin 501 257 gm 501 290 lin 485 291 gm 498 291 lin 485 293 gm 498 293 lin 499 291 gm 499 293 lin 501 291 gm 501 293 lin 499 294 gm 499 327 lin 501 294 gm 501 327 lin 485 328 gm 498 328 lin 485 330 gm 498 330 lin 499 328 gm 499 330 lin 501 328 gm 501 330 lin 499 331 gm 499 364 lin 501 331 gm 501 364 lin 485 365 gm 498 365 lin 485 367 gm 498 367 lin 499 365 gm 499 367 lin 501 365 gm 501 367 lin 499 368 gm 499 400 lin 501 368 gm 501 400 lin 485 401 gm 498 401 lin 485 403 gm 498 403 lin 499 401 gm 499 403 lin 501 401 gm 501 403 lin 499 404 gm 499 487 lin 501 404 gm 501 487 lin 485 488 gm 498 488 lin 485 490 gm 498 490 lin 499 488 gm 499 490 lin 501 488 gm 501 490 lin 499 491 gm 499 524 lin 501 491 gm 501 524 lin 485 525 gm 498 525 lin 485 527 gm 498 527 lin 501 525 gm 501 527 lin 499 527 gm 501 527 lin 499 525 gm 499 525 lin 499 525 lin 513 79 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (Fig)show 0 fs bu fc 2 F /|______Times-Roman fnt bn (.)show 1 fs bu fc 2 F /|______Times-Bold fnt bn (8)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( )show 2 fs bu fc 2 F /|______Times-Italic fnt bn (Static splitting, master does part of the search)show 530 101 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.02517 0. 32 0.00251 0.(We should allocate a worker on the master processor; unfortunately, Fig.8 shows that this is not)awidthshow 541 101 gm 0.28411 0. 32 0.02841 0.(a good idea, because a master process should be able to generate new tasks rapidly when other)awidthshow 552 101 gm 1.02462 0. 32 0.10246 0.(processors become idle: when a processor is shared by the master and a worker the answer)awidthshow 563 101 gm (times for master become too slow.)show 593 96 gm 1 fs 10 fz bu fc 2 F /|______Times-Bold fnt bn (Procs)show 593 145 gm (T\312\(sec\))show 593 203 gm (N\312\(nodi\))show 593 271 gm (S)show 593 308 gm (E)show 593 338 gm (Fpm)show 593 378 gm (SO)show 593 419 gm (SS\312\(nodi/sec\))show 593 502 gm (Sss)show 579 80 gm 0 gr 579 82 lin 579 80 gm 581 80 lin 581 82 gm 581 82 lin 581 82 lin 579 83 gm 579 131 lin 581 83 gm 581 131 lin 579 132 gm 579 134 lin 581 132 gm 581 134 lin 579 135 gm 579 182 lin 581 135 gm 581 182 lin 579 183 gm 579 185 lin 581 183 gm 581 185 lin 579 186 gm 579 253 lin 581 186 gm 581 253 lin 579 254 gm 579 256 lin 581 254 gm 581 256 lin 579 257 gm 579 290 lin 581 257 gm 581 290 lin 579 291 gm 579 293 lin 581 291 gm 581 293 lin 579 294 gm 579 327 lin 581 294 gm 581 327 lin 579 328 gm 579 330 lin 581 328 gm 581 330 lin 579 331 gm 579 364 lin 581 331 gm 581 364 lin 579 365 gm 579 367 lin 581 365 gm 581 367 lin 579 368 gm 579 400 lin 581 368 gm 581 400 lin 579 401 gm 579 403 lin 581 401 gm 581 403 lin 579 404 gm 579 487 lin 581 404 gm 581 487 lin 579 488 gm 579 490 lin 581 488 gm 581 490 lin 579 491 gm 579 524 lin 581 491 gm 581 524 lin 579 525 gm 579 527 lin 581 527 lin 581 525 gm 581 525 lin 581 525 lin 582 80 gm 595 80 lin 582 82 gm 595 82 lin 582 132 gm 595 132 lin 582 134 gm 595 134 lin 582 183 gm 595 183 lin 582 185 gm 595 185 lin 582 254 gm 595 254 lin 582 256 gm 595 256 lin 582 291 gm 595 291 lin 582 293 gm 595 293 lin 582 328 gm 595 328 lin 582 330 gm 595 330 lin 582 365 gm 595 365 lin 582 367 gm 595 367 lin 582 401 gm 595 401 lin 582 403 gm 595 403 lin 582 488 gm 595 488 lin 582 490 gm 595 490 lin 582 525 gm 595 525 lin 582 527 gm 595 527 lin 610 105 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn (1)show 610 149 gm (8301)show 610 203 gm (5347545)show 610 269 gm (---)show 610 306 gm (---)show 610 343 gm (---)show 610 380 gm (---)show 610 439 gm (644)show 610 503 gm (---)show 596 82 gm 0 gr 598 82 lin 596 80 gm 598 80 lin 596 83 gm 596 131 lin 598 83 gm 598 131 lin 596 134 gm 596 134 lin 598 132 gm 598 132 lin 596 132 gm 596 132 lin 598 134 gm 598 134 lin 596 135 gm 596 182 lin 598 135 gm 598 182 lin 596 185 gm 596 185 lin 598 183 gm 598 183 lin 596 183 gm 596 183 lin 598 185 gm 598 185 lin 596 186 gm 596 253 lin 598 186 gm 598 253 lin 596 256 gm 596 256 lin 598 254 gm 598 254 lin 596 254 gm 596 254 lin 598 256 gm 598 256 lin 596 257 gm 596 290 lin 598 257 gm 598 290 lin 596 293 gm 596 293 lin 598 291 gm 598 291 lin 596 291 gm 596 291 lin 598 293 gm 598 293 lin 596 294 gm 596 327 lin 598 294 gm 598 327 lin 596 330 gm 596 330 lin 598 328 gm 598 328 lin 596 328 gm 596 328 lin 598 330 gm 598 330 lin 596 331 gm 596 364 lin 598 331 gm 598 364 lin 596 367 gm 596 367 lin 598 365 gm 598 365 lin 596 365 gm 596 365 lin 598 367 gm 598 367 lin 596 368 gm 596 400 lin 598 368 gm 598 400 lin 596 403 gm 596 403 lin 598 401 gm 598 401 lin 596 401 gm 596 401 lin 598 403 gm 598 403 lin 596 404 gm 596 487 lin 598 404 gm 598 487 lin 596 490 gm 596 490 lin 598 488 gm 598 488 lin 596 488 gm 596 488 lin 598 490 gm 598 490 lin 596 491 gm 596 524 lin 598 491 gm 598 524 lin 596 527 gm 598 527 lin 596 525 gm 598 525 lin 599 80 gm 612 80 lin 599 82 gm 612 82 lin 599 132 gm 612 132 lin 599 134 gm 612 134 lin 599 183 gm 612 183 lin 599 185 gm 612 185 lin 599 254 gm 612 254 lin 599 256 gm 612 256 lin 599 291 gm 612 291 lin 599 293 gm 612 293 lin 599 328 gm 612 328 lin 599 330 gm 612 330 lin 599 365 gm 612 365 lin 599 367 gm 612 367 lin 599 401 gm 612 401 lin 599 403 gm 612 403 lin 599 488 gm 612 488 lin 599 490 gm 612 490 lin 599 525 gm 612 525 lin 599 527 gm 612 527 lin 625 105 gm F 1 setTxMode (3)show 625 149 gm (3298)show 625 203 gm (6156027)show 625 265 gm (2.52)show 625 302 gm (0.84)show 625 339 gm (0.96)show 625 376 gm (0.15)show 625 436 gm (1867)show 625 499 gm (2.90)show 613 82 gm 0 gr 613 82 lin 613 80 gm 613 80 lin 613 83 gm 613 131 lin 613 134 gm 613 134 lin 613 132 gm 613 132 lin 613 135 gm 613 182 lin 613 185 gm 613 185 lin 613 183 gm 613 183 lin 613 186 gm 613 253 lin 613 256 gm 613 256 lin 613 254 gm 613 254 lin 613 257 gm 613 290 lin 613 293 gm 613 293 lin 613 291 gm 613 291 lin 613 294 gm 613 327 lin 613 330 gm 613 330 lin 613 328 gm 613 328 lin 613 331 gm 613 364 lin 613 367 gm 613 367 lin 613 365 gm 613 365 lin 613 368 gm 613 400 lin 613 403 gm 613 403 lin 613 401 gm 613 401 lin 613 404 gm 613 487 lin 613 490 gm 613 490 lin 613 488 gm 613 488 lin 613 491 gm 613 524 lin 613 527 gm 613 527 lin 613 525 gm 613 525 lin 614 80 gm 627 80 lin 614 82 gm 627 82 lin 614 132 gm 627 132 lin 614 134 gm 627 134 lin 614 183 gm 627 183 lin 614 185 gm 627 185 lin 614 254 gm 627 254 lin 614 256 gm 627 256 lin 614 291 gm 627 291 lin 614 293 gm 627 293 lin 614 328 gm 627 328 lin 614 330 gm 627 330 lin 614 365 gm 627 365 lin 614 367 gm 627 367 lin 614 401 gm 627 401 lin 614 403 gm 627 403 lin 614 488 gm 627 488 lin 614 490 gm 627 490 lin 614 525 gm 627 525 lin 614 527 gm 627 527 lin 640 105 gm F 1 setTxMode (5)show 640 149 gm (2382)show 640 203 gm (6945194)show 640 265 gm (3.48)show 640 302 gm (0.70)show 640 339 gm (0.91)show 640 376 gm (0.30)show 640 436 gm (2916)show 640 499 gm (4.53)show 628 82 gm 0 gr 628 82 lin 628 80 gm 628 80 lin 628 83 gm 628 131 lin 628 134 gm 628 134 lin 628 132 gm 628 132 lin 628 135 gm 628 182 lin 628 185 gm 628 185 lin 628 183 gm 628 183 lin 628 186 gm 628 253 lin 628 256 gm 628 256 lin 628 254 gm 628 254 lin 628 257 gm 628 290 lin 628 293 gm 628 293 lin 628 291 gm 628 291 lin 628 294 gm 628 327 lin 628 330 gm 628 330 lin 628 328 gm 628 328 lin 628 331 gm 628 364 lin 628 367 gm 628 367 lin 628 365 gm 628 365 lin 628 368 gm 628 400 lin 628 403 gm 628 403 lin 628 401 gm 628 401 lin 628 404 gm 628 487 lin 628 490 gm 628 490 lin 628 488 gm 628 488 lin 628 491 gm 628 524 lin 628 527 gm 628 527 lin 628 525 gm 628 525 lin 629 80 gm 642 80 lin 629 82 gm 642 82 lin 629 132 gm 642 132 lin 629 134 gm 642 134 lin 629 183 gm 642 183 lin 629 185 gm 642 185 lin 629 254 gm 642 254 lin 629 256 gm 642 256 lin 629 291 gm 642 291 lin 629 293 gm 642 293 lin 629 328 gm 642 328 lin 629 330 gm 642 330 lin 629 365 gm 642 365 lin 629 367 gm 642 367 lin 629 401 gm 642 401 lin 629 403 gm 642 403 lin 629 488 gm 642 488 lin 629 490 gm 642 490 lin 629 525 gm 642 525 lin 629 527 gm 642 527 lin 655 105 gm F 1 setTxMode (7)show 655 149 gm (2064)show 655 203 gm (7524137)show 655 265 gm (4.02)show 655 302 gm (0.57)show 655 339 gm (0.81)show 655 376 gm (0.41)show 655 436 gm (3645)show 655 499 gm (5.66)show 643 82 gm 0 gr 643 82 lin 643 80 gm 643 80 lin 643 83 gm 643 131 lin 643 134 gm 643 134 lin 643 132 gm 643 132 lin 643 135 gm 643 182 lin 643 185 gm 643 185 lin 643 183 gm 643 183 lin 643 186 gm 643 253 lin 643 256 gm 643 256 lin 643 254 gm 643 254 lin 643 257 gm 643 290 lin 643 293 gm 643 293 lin 643 291 gm 643 291 lin 643 294 gm 643 327 lin 643 330 gm 643 330 lin 643 328 gm 643 328 lin 643 331 gm 643 364 lin 643 367 gm 643 367 lin 643 365 gm 643 365 lin 643 368 gm 643 400 lin 643 403 gm 643 403 lin 643 401 gm 643 401 lin 643 404 gm 643 487 lin 643 490 gm 643 490 lin 643 488 gm 643 488 lin 643 491 gm 643 524 lin 643 527 gm 643 527 lin 643 525 gm 643 525 lin 644 80 gm 657 80 lin 644 82 gm 657 82 lin 644 132 gm 657 132 lin 644 134 gm 657 134 lin 644 183 gm 657 183 lin 644 185 gm 657 185 lin 644 254 gm 657 254 lin 644 256 gm 657 256 lin 644 291 gm 657 291 lin 644 293 gm 657 293 lin 644 328 gm 657 328 lin 644 330 gm 657 330 lin 644 365 gm 657 365 lin 644 367 gm 657 367 lin 644 401 gm 657 401 lin 644 403 gm 657 403 lin 644 488 gm 657 488 lin 644 490 gm 657 490 lin 644 525 gm 657 525 lin 644 527 gm 657 527 lin 670 105 gm F 1 setTxMode (9)show 670 149 gm (1798)show 670 203 gm (8186074)show 670 265 gm (4.62)show 670 302 gm (0.51)show 670 339 gm (0.77)show 670 376 gm (0.53)show 670 436 gm (4553)show 670 499 gm (7.07)show 658 82 gm 0 gr 658 82 lin 658 80 gm 658 80 lin 658 83 gm 658 131 lin 658 134 gm 658 134 lin 658 132 gm 658 132 lin 658 135 gm 658 182 lin 658 185 gm 658 185 lin 658 183 gm 658 183 lin 658 186 gm 658 253 lin 658 256 gm 658 256 lin 658 254 gm 658 254 lin 658 257 gm 658 290 lin 658 293 gm 658 293 lin 658 291 gm 658 291 lin 658 294 gm 658 327 lin 658 330 gm 658 330 lin 658 328 gm 658 328 lin 658 331 gm 658 364 lin 658 367 gm 658 367 lin 658 365 gm 658 365 lin 658 368 gm 658 400 lin 658 403 gm 658 403 lin 658 401 gm 658 401 lin 658 404 gm 658 487 lin 658 490 gm 658 490 lin 658 488 gm 658 488 lin 658 491 gm 658 524 lin 658 527 gm 658 527 lin 658 525 gm 658 525 lin 659 80 gm 672 80 lin 659 82 gm 672 82 lin 659 132 gm 672 132 lin 659 134 gm 672 134 lin 659 183 gm 672 183 lin 659 185 gm 672 185 lin 659 254 gm 672 254 lin 659 256 gm 672 256 lin 659 291 gm 672 291 lin 659 293 gm 672 293 lin 659 328 gm 672 328 lin 659 330 gm 672 330 lin 659 365 gm 672 365 lin 659 367 gm 672 367 lin 659 401 gm 672 401 lin 659 403 gm 672 403 lin 659 488 gm 672 488 lin 659 490 gm 672 490 lin 659 525 gm 672 525 lin 659 527 gm 672 527 lin 685 103 gm F 1 setTxMode (11)show 685 149 gm (1751)show 685 203 gm (8746752)show 685 265 gm (4.74)show 685 302 gm (0.43)show 685 339 gm (0.71)show 685 376 gm (0.64)show 685 436 gm (4995)show 685 499 gm (7.75)show 673 82 gm 0 gr 673 82 lin 673 80 gm 673 80 lin 673 83 gm 673 131 lin 673 134 gm 673 134 lin 673 132 gm 673 132 lin 673 135 gm 673 182 lin 673 185 gm 673 185 lin 673 183 gm 673 183 lin 673 186 gm 673 253 lin 673 256 gm 673 256 lin 673 254 gm 673 254 lin 673 257 gm 673 290 lin 673 293 gm 673 293 lin 673 291 gm 673 291 lin 673 294 gm 673 327 lin 673 330 gm 673 330 lin 673 328 gm 673 328 lin 673 331 gm 673 364 lin 673 367 gm 673 367 lin 673 365 gm 673 365 lin 673 368 gm 673 400 lin 673 403 gm 673 403 lin 673 401 gm 673 401 lin 673 404 gm 673 487 lin 673 490 gm 673 490 lin 673 488 gm 673 488 lin 673 491 gm 673 524 lin 673 527 gm 673 527 lin 673 525 gm 673 525 lin 674 80 gm 687 80 lin 674 82 gm 687 82 lin 690 80 gm 690 82 lin 688 80 gm 690 80 lin 688 82 gm 688 82 lin 688 82 lin 688 83 gm 688 131 lin 690 83 gm 690 131 lin 674 132 gm 687 132 lin 674 134 gm 687 134 lin 688 132 gm 688 134 lin 690 132 gm 690 134 lin 688 135 gm 688 182 lin 690 135 gm 690 182 lin 674 183 gm 687 183 lin 674 185 gm 687 185 lin 688 183 gm 688 185 lin 690 183 gm 690 185 lin 688 186 gm 688 253 lin 690 186 gm 690 253 lin 674 254 gm 687 254 lin 674 256 gm 687 256 lin 688 254 gm 688 256 lin 690 254 gm 690 256 lin 688 257 gm 688 290 lin 690 257 gm 690 290 lin 674 291 gm 687 291 lin 674 293 gm 687 293 lin 688 291 gm 688 293 lin 690 291 gm 690 293 lin 688 294 gm 688 327 lin 690 294 gm 690 327 lin 674 328 gm 687 328 lin 674 330 gm 687 330 lin 688 328 gm 688 330 lin 690 328 gm 690 330 lin 688 331 gm 688 364 lin 690 331 gm 690 364 lin 674 365 gm 687 365 lin 674 367 gm 687 367 lin 688 365 gm 688 367 lin 690 365 gm 690 367 lin 688 368 gm 688 400 lin 690 368 gm 690 400 lin 674 401 gm 687 401 lin 674 403 gm 687 403 lin 688 401 gm 688 403 lin 690 401 gm 690 403 lin 688 404 gm 688 487 lin 690 404 gm 690 487 lin 674 488 gm 687 488 lin 674 490 gm 687 490 lin 688 488 gm 688 490 lin 690 488 gm 690 490 lin 688 491 gm 688 524 lin 690 491 gm 690 524 lin 674 525 gm 687 525 lin 674 527 gm 687 527 lin 690 525 gm 690 527 lin 688 527 gm 690 527 lin 688 525 gm 688 525 lin 688 525 lin 702 79 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (Fig.9)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( )show 2 fs bu fc 2 F /|______Times-Italic fnt bn (Static splitting, no master \(democratic cooperation\))show 718 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.72952 0. 32 0.07295 0.(The core algorithm can be rewritten to get a more efficient program: there is no need to maintain)awidthshow 729 79 gm 0.48248 0. 32 0.04824 0.(alive the master if the workers are able to handle the results. We call this variant of master-worker)awidthshow 740 79 gm -0.00064 0.(\322democratic coperation\323. Data shown in Fig.9 show an improvement with respect to the pure master-)ashow 751 79 gm 0.28015 0. 32 0.02801 0.(worker paradigm. However, such data also show that search overhead increased, because a\) there is)awidthshow F T cp %%Page: ? 11 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 336 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Helvetica fnt bn (A Comparison of Parallel Search Algorithms)show 773 79 gm (UBLCS-94-14)show 773 519 gm (9)show 118 79 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.70068 0. 32 0.07006 0.(one more process cooperating in the search, and b\) each worker starts executing a new task more)awidthshow 129 79 gm 0.61386 0. 32 0.06138 0.(rapidly, so it is less likely that it can use data from other explorers that finish while it is idle. The)awidthshow 140 79 gm 0.40039 0. 32 0.04003 0.(most important consideration is that the algorithms get similar results as we increase processors. In)awidthshow 151 79 gm 0.63476 0. 32 0.06347 0.(fact, let P be the total number of processors and E\(P\) number of exploring processors; let C\(P\)be:)awidthshow 0 0 pen 185 223 gm (nc 155 79 185 223 6 rc)kp 0 gr 185 223 lin psb currentpoint pse 155 79 gm 155 79 lin psb 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4608 div 960 3 -1 roll exch div scale currentpoint translate 64 44 translate -12 500 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Roman f1 (C) show 246 500 moveto (\() show 390 500 moveto (P) show 619 500 moveto (\)) show 829 500 moveto (=) show 1174 261 moveto (E) show 1408 261 moveto 224 ns (master) show 2091 261 moveto (-) show 2247 261 moveto (worker) show 2894 261 moveto 384 ns (\() show 3038 261 moveto (P) show 3267 261 moveto (\)) show 1418 793 moveto (E) show 1652 793 moveto 224 ns (democratic) show 2651 793 moveto 384 ns (\() show 2795 793 moveto (P) show 3024 793 moveto (\)) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1146 401 moveto 2262 0 rlineto stroke 3509 500 moveto (=) show 3854 261 moveto (P) show 4142 261 moveto (-) show 4306 261 moveto (1) show 4051 793 moveto (P) show 3826 401 moveto 663 0 rlineto stroke end pse 1 1 pen 172 223 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 2.31613 0. 32 0.23161 0.(. The ratio among production factors is proportional to C\(P\),)awidthshow 193 79 gm 4.52468 0. 32 0.45246 0.(whereas the ratio among value of search overhead is inversely proportional; since)awidthshow 0 0 pen 227 265 gm (nc 197 79 227 265 6 rc)kp 0 gr 227 265 lin psb currentpoint pse 197 79 gm 197 79 lin psb 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 5952 div 960 3 -1 roll exch div scale currentpoint translate 64 44 translate 12 500 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Roman f1 (lim) show 16 724 moveto 224 /Times-Italic f1 (p) show 142 724 moveto 224 /Symbol f1 (\256) show 383 724 moveto (\245) show 909 500 moveto 384 /Times-Italic f1 (C) show 1173 500 moveto 384 /Times-Roman f1 (\() show 1327 500 moveto 384 /Times-Italic f1 (P) show 1571 500 moveto 384 /Times-Roman f1 (\)) show 1788 500 moveto 384 /Symbol f1 (=) show 2064 500 moveto 384 /Times-Roman f1 (1) show 2594 500 moveto 384 /Times-Italic f1 (and) show 3574 500 moveto 384 /Times-Roman f1 (lim) show 3578 724 moveto 224 /Times-Italic f1 (p) show 3704 724 moveto 224 /Symbol f1 (\256) show 3945 724 moveto (\245) show 4798 261 moveto 384 /Times-Roman f1 (1) show 4503 793 moveto 384 /Times-Italic f1 (C) show 4767 793 moveto 384 /Times-Roman f1 (\() show 4921 793 moveto 384 /Times-Italic f1 (P) show 5165 793 moveto 384 /Times-Roman f1 (\)) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 4483 401 moveto 823 0 rlineto stroke 5414 500 moveto 384 /Symbol f1 (=) show 5690 500 moveto 384 /Times-Roman f1 (1) show end pse 1 1 pen 214 265 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode ( the two algorithms are asyntotically equivalent.)show 254 79 gm 1 fs 12 fz bu fc 2 F /|______Times-Bold fnt bn (4.1 Ordered game trees: iterative deepening and top level sorting)show 267 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.68984 0. 32 0.06898 0.(In the algorithms presented above there is no sorting of nodes; however, it is well known that the)awidthshow 282 79 gm 2.09381 0. 32 0.20938 0.(execution of )awidthshow 282 143 gm bu fc 2 F /|______Symbol fnt bn 0.69818 0.(ab)ashow bu fc 2 F /|______Times-Roman fnt bn 1.98272 0. 32 0.19827 0.( algorithm improves if game tree nodes are ordered [MarCam82]. We have)awidthshow 294 79 gm 0.63858 0. 32 0.06385 0.(implemented such a sorting, and the resulting search algorithm has been tested with the following)awidthshow 305 79 gm 0.10040 0. 32 0.01004 0.(parameters for iterative deepening: INIT=2-plies, MAX=5-plies; thresold for parallel search: 3)awidthshow 305 496 gm (-plies.)show 320 79 gm 0.18295 0. 32 0.01829 0.(The sequential algorithm we used for comparison is )awidthshow bu fc 2 F /|______Symbol fnt bn 0.06732 0.(ab)ashow bu fc 2 F /|______Times-Roman fnt bn 0.18188 0. 32 0.01818 0.( with iterative deepening and same INIT and)awidthshow 332 79 gm (MAX.)show 361 96 gm 1 fs 10 fz bu fc 2 F /|______Times-Bold fnt bn (Procs)show 361 145 gm (T\312\(sec\))show 361 200 gm (N\312\(nodes\))show 361 271 gm (S)show 361 308 gm (E)show 361 338 gm (Fpm)show 361 378 gm (SO)show 361 418 gm (SS )show 9 fz bu fc 2 F /|______Times-Bold fnt bn (\(nodes/sec\))show 361 502 gm 10 fz bu fc 2 F /|______Times-Bold fnt bn (Sss)show 347 80 gm 0 gr 347 82 lin 347 80 gm 349 80 lin 349 82 gm 349 82 lin 349 82 lin 347 83 gm 347 131 lin 349 83 gm 349 131 lin 347 132 gm 347 134 lin 349 132 gm 349 134 lin 347 135 gm 347 182 lin 349 135 gm 349 182 lin 347 183 gm 347 185 lin 349 183 gm 349 185 lin 347 186 gm 347 253 lin 349 186 gm 349 253 lin 347 254 gm 347 256 lin 349 254 gm 349 256 lin 347 257 gm 347 290 lin 349 257 gm 349 290 lin 347 291 gm 347 293 lin 349 291 gm 349 293 lin 347 294 gm 347 327 lin 349 294 gm 349 327 lin 347 328 gm 347 330 lin 349 328 gm 349 330 lin 347 331 gm 347 364 lin 349 331 gm 349 364 lin 347 365 gm 347 367 lin 349 365 gm 349 367 lin 347 368 gm 347 400 lin 349 368 gm 349 400 lin 347 401 gm 347 403 lin 349 401 gm 349 403 lin 347 404 gm 347 487 lin 349 404 gm 349 487 lin 347 488 gm 347 490 lin 349 488 gm 349 490 lin 347 491 gm 347 524 lin 349 491 gm 349 524 lin 347 525 gm 347 527 lin 349 527 lin 349 525 gm 349 525 lin 349 525 lin 350 80 gm 363 80 lin 350 82 gm 363 82 lin 350 132 gm 363 132 lin 350 134 gm 363 134 lin 350 183 gm 363 183 lin 350 185 gm 363 185 lin 350 254 gm 363 254 lin 350 256 gm 363 256 lin 350 291 gm 363 291 lin 350 293 gm 363 293 lin 350 328 gm 363 328 lin 350 330 gm 363 330 lin 350 365 gm 363 365 lin 350 367 gm 363 367 lin 350 401 gm 363 401 lin 350 403 gm 363 403 lin 350 488 gm 363 488 lin 350 490 gm 363 490 lin 350 525 gm 363 525 lin 350 527 gm 363 527 lin 378 105 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn (1)show 378 149 gm (6740)show 378 203 gm (4529971)show 378 269 gm (---)show 378 306 gm (---)show 378 343 gm (---)show 378 380 gm (---)show 378 439 gm (672)show 378 503 gm (---)show 364 82 gm 0 gr 366 82 lin 364 80 gm 366 80 lin 364 83 gm 364 131 lin 366 83 gm 366 131 lin 364 134 gm 364 134 lin 366 132 gm 366 132 lin 364 132 gm 364 132 lin 366 134 gm 366 134 lin 364 135 gm 364 182 lin 366 135 gm 366 182 lin 364 185 gm 364 185 lin 366 183 gm 366 183 lin 364 183 gm 364 183 lin 366 185 gm 366 185 lin 364 186 gm 364 253 lin 366 186 gm 366 253 lin 364 256 gm 364 256 lin 366 254 gm 366 254 lin 364 254 gm 364 254 lin 366 256 gm 366 256 lin 364 257 gm 364 290 lin 366 257 gm 366 290 lin 364 293 gm 364 293 lin 366 291 gm 366 291 lin 364 291 gm 364 291 lin 366 293 gm 366 293 lin 364 294 gm 364 327 lin 366 294 gm 366 327 lin 364 330 gm 364 330 lin 366 328 gm 366 328 lin 364 328 gm 364 328 lin 366 330 gm 366 330 lin 364 331 gm 364 364 lin 366 331 gm 366 364 lin 364 367 gm 364 367 lin 366 365 gm 366 365 lin 364 365 gm 364 365 lin 366 367 gm 366 367 lin 364 368 gm 364 400 lin 366 368 gm 366 400 lin 364 403 gm 364 403 lin 366 401 gm 366 401 lin 364 401 gm 364 401 lin 366 403 gm 366 403 lin 364 404 gm 364 487 lin 366 404 gm 366 487 lin 364 490 gm 364 490 lin 366 488 gm 366 488 lin 364 488 gm 364 488 lin 366 490 gm 366 490 lin 364 491 gm 364 524 lin 366 491 gm 366 524 lin 364 527 gm 366 527 lin 364 525 gm 366 525 lin 367 80 gm 380 80 lin 367 82 gm 380 82 lin 367 132 gm 380 132 lin 367 134 gm 380 134 lin 367 183 gm 380 183 lin 367 185 gm 380 185 lin 367 254 gm 380 254 lin 367 256 gm 380 256 lin 367 291 gm 380 291 lin 367 293 gm 380 293 lin 367 328 gm 380 328 lin 367 330 gm 380 330 lin 367 365 gm 380 365 lin 367 367 gm 380 367 lin 367 401 gm 380 401 lin 367 403 gm 380 403 lin 367 488 gm 380 488 lin 367 490 gm 380 490 lin 367 525 gm 380 525 lin 367 527 gm 380 527 lin 393 105 gm F 1 setTxMode (3)show 393 149 gm (2884)show 393 203 gm (5415125)show 393 265 gm (2.34)show 393 302 gm (0.78)show 393 339 gm (0.94)show 393 376 gm (0.20)show 393 436 gm (1878)show 393 499 gm (2.79)show 381 82 gm 0 gr 381 82 lin 381 80 gm 381 80 lin 381 83 gm 381 131 lin 381 134 gm 381 134 lin 381 132 gm 381 132 lin 381 135 gm 381 182 lin 381 185 gm 381 185 lin 381 183 gm 381 183 lin 381 186 gm 381 253 lin 381 256 gm 381 256 lin 381 254 gm 381 254 lin 381 257 gm 381 290 lin 381 293 gm 381 293 lin 381 291 gm 381 291 lin 381 294 gm 381 327 lin 381 330 gm 381 330 lin 381 328 gm 381 328 lin 381 331 gm 381 364 lin 381 367 gm 381 367 lin 381 365 gm 381 365 lin 381 368 gm 381 400 lin 381 403 gm 381 403 lin 381 401 gm 381 401 lin 381 404 gm 381 487 lin 381 490 gm 381 490 lin 381 488 gm 381 488 lin 381 491 gm 381 524 lin 381 527 gm 381 527 lin 381 525 gm 381 525 lin 382 80 gm 395 80 lin 382 82 gm 395 82 lin 382 132 gm 395 132 lin 382 134 gm 395 134 lin 382 183 gm 395 183 lin 382 185 gm 395 185 lin 382 254 gm 395 254 lin 382 256 gm 395 256 lin 382 291 gm 395 291 lin 382 293 gm 395 293 lin 382 328 gm 395 328 lin 382 330 gm 395 330 lin 382 365 gm 395 365 lin 382 367 gm 395 367 lin 382 401 gm 395 401 lin 382 403 gm 395 403 lin 382 488 gm 395 488 lin 382 490 gm 395 490 lin 382 525 gm 395 525 lin 382 527 gm 395 527 lin 408 105 gm F 1 setTxMode (5)show 408 149 gm (2229)show 408 203 gm (6307062)show 408 265 gm (3.02)show 408 302 gm (0.60)show 408 339 gm (0.87)show 408 376 gm (0.39)show 408 436 gm (2830)show 408 499 gm (4.21)show 396 82 gm 0 gr 396 82 lin 396 80 gm 396 80 lin 396 83 gm 396 131 lin 396 134 gm 396 134 lin 396 132 gm 396 132 lin 396 135 gm 396 182 lin 396 185 gm 396 185 lin 396 183 gm 396 183 lin 396 186 gm 396 253 lin 396 256 gm 396 256 lin 396 254 gm 396 254 lin 396 257 gm 396 290 lin 396 293 gm 396 293 lin 396 291 gm 396 291 lin 396 294 gm 396 327 lin 396 330 gm 396 330 lin 396 328 gm 396 328 lin 396 331 gm 396 364 lin 396 367 gm 396 367 lin 396 365 gm 396 365 lin 396 368 gm 396 400 lin 396 403 gm 396 403 lin 396 401 gm 396 401 lin 396 404 gm 396 487 lin 396 490 gm 396 490 lin 396 488 gm 396 488 lin 396 491 gm 396 524 lin 396 527 gm 396 527 lin 396 525 gm 396 525 lin 397 80 gm 410 80 lin 397 82 gm 410 82 lin 397 132 gm 410 132 lin 397 134 gm 410 134 lin 397 183 gm 410 183 lin 397 185 gm 410 185 lin 397 254 gm 410 254 lin 397 256 gm 410 256 lin 397 291 gm 410 291 lin 397 293 gm 410 293 lin 397 328 gm 410 328 lin 397 330 gm 410 330 lin 397 365 gm 410 365 lin 397 367 gm 410 367 lin 397 401 gm 410 401 lin 397 403 gm 410 403 lin 397 488 gm 410 488 lin 397 490 gm 410 490 lin 397 525 gm 410 525 lin 397 527 gm 410 527 lin 423 105 gm F 1 setTxMode (7)show 423 149 gm (2007)show 423 203 gm (7317370)show 423 265 gm (3.36)show 423 302 gm (0.48)show 423 339 gm (0.80)show 423 376 gm (0.62)show 423 436 gm (3646)show 423 499 gm (5.42)show 411 82 gm 0 gr 411 82 lin 411 80 gm 411 80 lin 411 83 gm 411 131 lin 411 134 gm 411 134 lin 411 132 gm 411 132 lin 411 135 gm 411 182 lin 411 185 gm 411 185 lin 411 183 gm 411 183 lin 411 186 gm 411 253 lin 411 256 gm 411 256 lin 411 254 gm 411 254 lin 411 257 gm 411 290 lin 411 293 gm 411 293 lin 411 291 gm 411 291 lin 411 294 gm 411 327 lin 411 330 gm 411 330 lin 411 328 gm 411 328 lin 411 331 gm 411 364 lin 411 367 gm 411 367 lin 411 365 gm 411 365 lin 411 368 gm 411 400 lin 411 403 gm 411 403 lin 411 401 gm 411 401 lin 411 404 gm 411 487 lin 411 490 gm 411 490 lin 411 488 gm 411 488 lin 411 491 gm 411 524 lin 411 527 gm 411 527 lin 411 525 gm 411 525 lin 412 80 gm 425 80 lin 412 82 gm 425 82 lin 412 132 gm 425 132 lin 412 134 gm 425 134 lin 412 183 gm 425 183 lin 412 185 gm 425 185 lin 412 254 gm 425 254 lin 412 256 gm 425 256 lin 412 291 gm 425 291 lin 412 293 gm 425 293 lin 412 328 gm 425 328 lin 412 330 gm 425 330 lin 412 365 gm 425 365 lin 412 367 gm 425 367 lin 412 401 gm 425 401 lin 412 403 gm 425 403 lin 412 488 gm 425 488 lin 412 490 gm 425 490 lin 412 525 gm 425 525 lin 412 527 gm 425 527 lin 438 105 gm F 1 setTxMode (9)show 438 149 gm (1839)show 438 203 gm (8187769)show 438 265 gm (3.67)show 438 302 gm (0.41)show 438 339 gm (0.75)show 438 376 gm (0.81)show 438 436 gm (4452)show 438 499 gm (6.62)show 426 82 gm 0 gr 426 82 lin 426 80 gm 426 80 lin 426 83 gm 426 131 lin 426 134 gm 426 134 lin 426 132 gm 426 132 lin 426 135 gm 426 182 lin 426 185 gm 426 185 lin 426 183 gm 426 183 lin 426 186 gm 426 253 lin 426 256 gm 426 256 lin 426 254 gm 426 254 lin 426 257 gm 426 290 lin 426 293 gm 426 293 lin 426 291 gm 426 291 lin 426 294 gm 426 327 lin 426 330 gm 426 330 lin 426 328 gm 426 328 lin 426 331 gm 426 364 lin 426 367 gm 426 367 lin 426 365 gm 426 365 lin 426 368 gm 426 400 lin 426 403 gm 426 403 lin 426 401 gm 426 401 lin 426 404 gm 426 487 lin 426 490 gm 426 490 lin 426 488 gm 426 488 lin 426 491 gm 426 524 lin 426 527 gm 426 527 lin 426 525 gm 426 525 lin 427 80 gm 440 80 lin 427 82 gm 440 82 lin 427 132 gm 440 132 lin 427 134 gm 440 134 lin 427 183 gm 440 183 lin 427 185 gm 440 185 lin 427 254 gm 440 254 lin 427 256 gm 440 256 lin 427 291 gm 440 291 lin 427 293 gm 440 293 lin 427 328 gm 440 328 lin 427 330 gm 440 330 lin 427 365 gm 440 365 lin 427 367 gm 440 367 lin 427 401 gm 440 401 lin 427 403 gm 440 403 lin 427 488 gm 440 488 lin 427 490 gm 440 490 lin 427 525 gm 440 525 lin 427 527 gm 440 527 lin 453 103 gm F 1 setTxMode (11)show 453 149 gm (1825)show 453 203 gm (8980505)show 453 265 gm (3.69)show 453 302 gm (0.34)show 453 339 gm (0.71)show 453 376 gm (0.98)show 453 436 gm (4921)show 453 499 gm (7.32)show 441 82 gm 0 gr 441 82 lin 441 80 gm 441 80 lin 441 83 gm 441 131 lin 441 134 gm 441 134 lin 441 132 gm 441 132 lin 441 135 gm 441 182 lin 441 185 gm 441 185 lin 441 183 gm 441 183 lin 441 186 gm 441 253 lin 441 256 gm 441 256 lin 441 254 gm 441 254 lin 441 257 gm 441 290 lin 441 293 gm 441 293 lin 441 291 gm 441 291 lin 441 294 gm 441 327 lin 441 330 gm 441 330 lin 441 328 gm 441 328 lin 441 331 gm 441 364 lin 441 367 gm 441 367 lin 441 365 gm 441 365 lin 441 368 gm 441 400 lin 441 403 gm 441 403 lin 441 401 gm 441 401 lin 441 404 gm 441 487 lin 441 490 gm 441 490 lin 441 488 gm 441 488 lin 441 491 gm 441 524 lin 441 527 gm 441 527 lin 441 525 gm 441 525 lin 442 80 gm 455 80 lin 442 82 gm 455 82 lin 458 80 gm 458 82 lin 456 80 gm 458 80 lin 456 82 gm 456 82 lin 456 82 lin 456 83 gm 456 131 lin 458 83 gm 458 131 lin 442 132 gm 455 132 lin 442 134 gm 455 134 lin 456 132 gm 456 134 lin 458 132 gm 458 134 lin 456 135 gm 456 182 lin 458 135 gm 458 182 lin 442 183 gm 455 183 lin 442 185 gm 455 185 lin 456 183 gm 456 185 lin 458 183 gm 458 185 lin 456 186 gm 456 253 lin 458 186 gm 458 253 lin 442 254 gm 455 254 lin 442 256 gm 455 256 lin 456 254 gm 456 256 lin 458 254 gm 458 256 lin 456 257 gm 456 290 lin 458 257 gm 458 290 lin 442 291 gm 455 291 lin 442 293 gm 455 293 lin 456 291 gm 456 293 lin 458 291 gm 458 293 lin 456 294 gm 456 327 lin 458 294 gm 458 327 lin 442 328 gm 455 328 lin 442 330 gm 455 330 lin 456 328 gm 456 330 lin 458 328 gm 458 330 lin 456 331 gm 456 364 lin 458 331 gm 458 364 lin 442 365 gm 455 365 lin 442 367 gm 455 367 lin 456 365 gm 456 367 lin 458 365 gm 458 367 lin 456 368 gm 456 400 lin 458 368 gm 458 400 lin 442 401 gm 455 401 lin 442 403 gm 455 403 lin 456 401 gm 456 403 lin 458 401 gm 458 403 lin 456 404 gm 456 487 lin 458 404 gm 458 487 lin 442 488 gm 455 488 lin 442 490 gm 455 490 lin 456 488 gm 456 490 lin 458 488 gm 458 490 lin 456 491 gm 456 524 lin 458 491 gm 458 524 lin 442 525 gm 455 525 lin 442 527 gm 455 527 lin 458 525 gm 458 527 lin 456 527 gm 458 527 lin 456 525 gm 456 525 lin 456 525 lin 470 79 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (Fig.10)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( )show 2 fs bu fc 2 F /|______Times-Italic fnt bn (Basic algorithm, iterative deepening and top-level sorting)show 486 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 1.85195 0. 32 0.18519 0.(The most impressive result in Fig.10 is the increasing of search overhead SO \(98% with 11)awidthshow 497 79 gm 0.59921 0. 32 0.05992 0.(processors\). The number of visited nodes is larger for 9 and 11 processors. On the other hand, the)awidthshow 508 79 gm 1.22573 0. 32 0.12257 0.(sequential version benefits from the new heuristics: the visited nodes are decreasd of 17%. We)awidthshow 519 79 gm 1.15554 0. 32 0.11555 0.(explain this with the fact that parallel search initially cannot gain any advantage from top level)awidthshow 530 79 gm (sorting, since all processes start simultaneously with initial score equal to -)show currentfont SwToSym (\245)show setfont (.)show 541 79 gm 0.40695 0. 32 0.04069 0.(Moreover, with respect to no iterative deepening, in this case visited nodes include also all internal)awidthshow 552 79 gm 0.11657 0. 32 0.01165 0.(nodes: this explains the total count with 11 processors. However, the average production factor Fpm)awidthshow 563 79 gm (decreases of 2%: there is a larger synchronization overhead due to search in the internal tree.)show 593 79 gm 1 fs 12 fz bu fc 2 F /|______Times-Bold fnt bn (4.2 Reducing the search overhead)show 606 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn (Search overhead is caused:)show 618 88 gm (\245\312by lack of sharing of score during search;)show 631 88 gm (\245\312initial score = -)show currentfont SwToSym (\245)show setfont ( for the first N)show 9 fz bu fc 2 F /|______Times-Roman fnt bn (w)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( tasks \(N)show 631 277 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (w)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( = # explorers\).)show 643 79 gm 0.40771 0. 32 0.04077 0.(We try to overcome such problems introducing a tuple storing a global score that all local searches)awidthshow 654 79 gm 1.10519 0. 32 0.11051 0.(can query. The global score tuple that can be read at any moment, but we must be careful with)awidthshow 665 79 gm 1.13174 0. 32 0.11317 0.(reading such a tuple, because it may be a very expensive operation. Thus, we try to make only)awidthshow 676 79 gm 0.11413 0. 32 0.01141 0.("useful" readings: after each reading of the global score the explorer puts in the tuple space a private)awidthshow 687 79 gm 0.35781 0. 32 0.03578 0.(tuple. When a worker modifies the global score it removes all private tuples, so that they can know)awidthshow 699 79 gm 0.66818 0. 32 0.06681 0.(when an update was done. In C-Linda )awidthshow bu fc 2 F /|______Courier fnt bn 0.27516 0.(out)ashow bu fc 2 F /|______Times-Roman fnt bn 0.73806 0. 32 0.07380 0.( operations are local and inexpensive, whereas )awidthshow bu fc 2 F /|______Courier fnt bn 0.27517 0.(in)ashow bu fc 2 F /|______Times-Roman fnt bn 0.51879 0. 32 0.05187 0.( are)awidthshow 710 79 gm 0.23971 0. 32 0.02397 0.(based on broadcasting and are expensive. Deletion of private tuples is expensive as well, but it does)awidthshow 721 79 gm (not happen frequently. Fig.11 shows the evaluation of such an algorithm.)show F T cp %%Page: ? 12 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 336 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Helvetica fnt bn (A Comparison of Parallel Search Algorithms)show 773 79 gm (UBLCS-94-14)show 773 514 gm (10)show 124 96 gm 1 fs bu fc 2 F /|______Times-Bold fnt bn (Procs)show 124 145 gm (T\312\(sec\))show 124 200 gm (N\312\(nodes\))show 124 271 gm (S)show 124 308 gm (E)show 124 338 gm (Fpm)show 124 378 gm (SO)show 124 416 gm (SS\312\(nodes/sec\))show 124 502 gm (Sss)show 110 80 gm 0 gr 110 82 lin 110 80 gm 112 80 lin 112 82 gm 112 82 lin 112 82 lin 110 83 gm 110 131 lin 112 83 gm 112 131 lin 110 132 gm 110 134 lin 112 132 gm 112 134 lin 110 135 gm 110 182 lin 112 135 gm 112 182 lin 110 183 gm 110 185 lin 112 183 gm 112 185 lin 110 186 gm 110 253 lin 112 186 gm 112 253 lin 110 254 gm 110 256 lin 112 254 gm 112 256 lin 110 257 gm 110 290 lin 112 257 gm 112 290 lin 110 291 gm 110 293 lin 112 291 gm 112 293 lin 110 294 gm 110 327 lin 112 294 gm 112 327 lin 110 328 gm 110 330 lin 112 328 gm 112 330 lin 110 331 gm 110 364 lin 112 331 gm 112 364 lin 110 365 gm 110 367 lin 112 365 gm 112 367 lin 110 368 gm 110 400 lin 112 368 gm 112 400 lin 110 401 gm 110 403 lin 112 401 gm 112 403 lin 110 404 gm 110 487 lin 112 404 gm 112 487 lin 110 488 gm 110 490 lin 112 488 gm 112 490 lin 110 491 gm 110 524 lin 112 491 gm 112 524 lin 110 525 gm 110 527 lin 112 527 lin 112 525 gm 112 525 lin 112 525 lin 113 80 gm 126 80 lin 113 82 gm 126 82 lin 113 132 gm 126 132 lin 113 134 gm 126 134 lin 113 183 gm 126 183 lin 113 185 gm 126 185 lin 113 254 gm 126 254 lin 113 256 gm 126 256 lin 113 291 gm 126 291 lin 113 293 gm 126 293 lin 113 328 gm 126 328 lin 113 330 gm 126 330 lin 113 365 gm 126 365 lin 113 367 gm 126 367 lin 113 401 gm 126 401 lin 113 403 gm 126 403 lin 113 488 gm 126 488 lin 113 490 gm 126 490 lin 113 525 gm 126 525 lin 113 527 gm 126 527 lin 141 105 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn (1)show 141 149 gm (6740)show 141 203 gm (4529971)show 141 269 gm (---)show 141 306 gm (---)show 141 343 gm (---)show 141 380 gm (---)show 141 439 gm (672)show 141 503 gm (---)show 127 82 gm 0 gr 129 82 lin 127 80 gm 129 80 lin 127 83 gm 127 131 lin 129 83 gm 129 131 lin 127 134 gm 127 134 lin 129 132 gm 129 132 lin 127 132 gm 127 132 lin 129 134 gm 129 134 lin 127 135 gm 127 182 lin 129 135 gm 129 182 lin 127 185 gm 127 185 lin 129 183 gm 129 183 lin 127 183 gm 127 183 lin 129 185 gm 129 185 lin 127 186 gm 127 253 lin 129 186 gm 129 253 lin 127 256 gm 127 256 lin 129 254 gm 129 254 lin 127 254 gm 127 254 lin 129 256 gm 129 256 lin 127 257 gm 127 290 lin 129 257 gm 129 290 lin 127 293 gm 127 293 lin 129 291 gm 129 291 lin 127 291 gm 127 291 lin 129 293 gm 129 293 lin 127 294 gm 127 327 lin 129 294 gm 129 327 lin 127 330 gm 127 330 lin 129 328 gm 129 328 lin 127 328 gm 127 328 lin 129 330 gm 129 330 lin 127 331 gm 127 364 lin 129 331 gm 129 364 lin 127 367 gm 127 367 lin 129 365 gm 129 365 lin 127 365 gm 127 365 lin 129 367 gm 129 367 lin 127 368 gm 127 400 lin 129 368 gm 129 400 lin 127 403 gm 127 403 lin 129 401 gm 129 401 lin 127 401 gm 127 401 lin 129 403 gm 129 403 lin 127 404 gm 127 487 lin 129 404 gm 129 487 lin 127 490 gm 127 490 lin 129 488 gm 129 488 lin 127 488 gm 127 488 lin 129 490 gm 129 490 lin 127 491 gm 127 524 lin 129 491 gm 129 524 lin 127 527 gm 129 527 lin 127 525 gm 129 525 lin 130 80 gm 143 80 lin 130 82 gm 143 82 lin 130 132 gm 143 132 lin 130 134 gm 143 134 lin 130 183 gm 143 183 lin 130 185 gm 143 185 lin 130 254 gm 143 254 lin 130 256 gm 143 256 lin 130 291 gm 143 291 lin 130 293 gm 143 293 lin 130 328 gm 143 328 lin 130 330 gm 143 330 lin 130 365 gm 143 365 lin 130 367 gm 143 367 lin 130 401 gm 143 401 lin 130 403 gm 143 403 lin 130 488 gm 143 488 lin 130 490 gm 143 490 lin 130 525 gm 143 525 lin 130 527 gm 143 527 lin 156 105 gm F 1 setTxMode (3)show 156 149 gm (2689)show 156 203 gm (4995937)show 156 265 gm (2.51)show 156 302 gm (0.84)show 156 339 gm (0.94)show 156 376 gm (0.10)show 156 436 gm (1858)show 156 499 gm (2.76)show 144 82 gm 0 gr 144 82 lin 144 80 gm 144 80 lin 144 83 gm 144 131 lin 144 134 gm 144 134 lin 144 132 gm 144 132 lin 144 135 gm 144 182 lin 144 185 gm 144 185 lin 144 183 gm 144 183 lin 144 186 gm 144 253 lin 144 256 gm 144 256 lin 144 254 gm 144 254 lin 144 257 gm 144 290 lin 144 293 gm 144 293 lin 144 291 gm 144 291 lin 144 294 gm 144 327 lin 144 330 gm 144 330 lin 144 328 gm 144 328 lin 144 331 gm 144 364 lin 144 367 gm 144 367 lin 144 365 gm 144 365 lin 144 368 gm 144 400 lin 144 403 gm 144 403 lin 144 401 gm 144 401 lin 144 404 gm 144 487 lin 144 490 gm 144 490 lin 144 488 gm 144 488 lin 144 491 gm 144 524 lin 144 527 gm 144 527 lin 144 525 gm 144 525 lin 145 80 gm 158 80 lin 145 82 gm 158 82 lin 145 132 gm 158 132 lin 145 134 gm 158 134 lin 145 183 gm 158 183 lin 145 185 gm 158 185 lin 145 254 gm 158 254 lin 145 256 gm 158 256 lin 145 291 gm 158 291 lin 145 293 gm 158 293 lin 145 328 gm 158 328 lin 145 330 gm 158 330 lin 145 365 gm 158 365 lin 145 367 gm 158 367 lin 145 401 gm 158 401 lin 145 403 gm 158 403 lin 145 488 gm 158 488 lin 145 490 gm 158 490 lin 145 525 gm 158 525 lin 145 527 gm 158 527 lin 171 105 gm F 1 setTxMode (5)show 171 149 gm (1854)show 171 203 gm (5346599)show 171 265 gm (3.64)show 171 302 gm (0.73)show 171 339 gm (0.88)show 171 376 gm (0.18)show 171 436 gm (2884)show 171 499 gm (4.29)show 159 82 gm 0 gr 159 82 lin 159 80 gm 159 80 lin 159 83 gm 159 131 lin 159 134 gm 159 134 lin 159 132 gm 159 132 lin 159 135 gm 159 182 lin 159 185 gm 159 185 lin 159 183 gm 159 183 lin 159 186 gm 159 253 lin 159 256 gm 159 256 lin 159 254 gm 159 254 lin 159 257 gm 159 290 lin 159 293 gm 159 293 lin 159 291 gm 159 291 lin 159 294 gm 159 327 lin 159 330 gm 159 330 lin 159 328 gm 159 328 lin 159 331 gm 159 364 lin 159 367 gm 159 367 lin 159 365 gm 159 365 lin 159 368 gm 159 400 lin 159 403 gm 159 403 lin 159 401 gm 159 401 lin 159 404 gm 159 487 lin 159 490 gm 159 490 lin 159 488 gm 159 488 lin 159 491 gm 159 524 lin 159 527 gm 159 527 lin 159 525 gm 159 525 lin 160 80 gm 173 80 lin 160 82 gm 173 82 lin 160 132 gm 173 132 lin 160 134 gm 173 134 lin 160 183 gm 173 183 lin 160 185 gm 173 185 lin 160 254 gm 173 254 lin 160 256 gm 173 256 lin 160 291 gm 173 291 lin 160 293 gm 173 293 lin 160 328 gm 173 328 lin 160 330 gm 173 330 lin 160 365 gm 173 365 lin 160 367 gm 173 367 lin 160 401 gm 173 401 lin 160 403 gm 173 403 lin 160 488 gm 173 488 lin 160 490 gm 173 490 lin 160 525 gm 173 525 lin 160 527 gm 173 527 lin 186 105 gm F 1 setTxMode (7)show 186 149 gm (1485)show 186 203 gm (5634915)show 186 265 gm (4.54)show 186 302 gm (0.65)show 186 339 gm (0.81)show 186 376 gm (0.24)show 186 436 gm (3795)show 186 499 gm (5.65)show 174 82 gm 0 gr 174 82 lin 174 80 gm 174 80 lin 174 83 gm 174 131 lin 174 134 gm 174 134 lin 174 132 gm 174 132 lin 174 135 gm 174 182 lin 174 185 gm 174 185 lin 174 183 gm 174 183 lin 174 186 gm 174 253 lin 174 256 gm 174 256 lin 174 254 gm 174 254 lin 174 257 gm 174 290 lin 174 293 gm 174 293 lin 174 291 gm 174 291 lin 174 294 gm 174 327 lin 174 330 gm 174 330 lin 174 328 gm 174 328 lin 174 331 gm 174 364 lin 174 367 gm 174 367 lin 174 365 gm 174 365 lin 174 368 gm 174 400 lin 174 403 gm 174 403 lin 174 401 gm 174 401 lin 174 404 gm 174 487 lin 174 490 gm 174 490 lin 174 488 gm 174 488 lin 174 491 gm 174 524 lin 174 527 gm 174 527 lin 174 525 gm 174 525 lin 175 80 gm 188 80 lin 175 82 gm 188 82 lin 175 132 gm 188 132 lin 175 134 gm 188 134 lin 175 183 gm 188 183 lin 175 185 gm 188 185 lin 175 254 gm 188 254 lin 175 256 gm 188 256 lin 175 291 gm 188 291 lin 175 293 gm 188 293 lin 175 328 gm 188 328 lin 175 330 gm 188 330 lin 175 365 gm 188 365 lin 175 367 gm 188 367 lin 175 401 gm 188 401 lin 175 403 gm 188 403 lin 175 488 gm 188 488 lin 175 490 gm 188 490 lin 175 525 gm 188 525 lin 175 527 gm 188 527 lin 201 105 gm F 1 setTxMode (9)show 201 149 gm (1315)show 201 203 gm (5936185)show 201 265 gm (5.13)show 201 302 gm (0.57)show 201 339 gm (0.77)show 201 376 gm (0.31)show 201 436 gm (4514)show 201 499 gm (6.72)show 189 82 gm 0 gr 189 82 lin 189 80 gm 189 80 lin 189 83 gm 189 131 lin 189 134 gm 189 134 lin 189 132 gm 189 132 lin 189 135 gm 189 182 lin 189 185 gm 189 185 lin 189 183 gm 189 183 lin 189 186 gm 189 253 lin 189 256 gm 189 256 lin 189 254 gm 189 254 lin 189 257 gm 189 290 lin 189 293 gm 189 293 lin 189 291 gm 189 291 lin 189 294 gm 189 327 lin 189 330 gm 189 330 lin 189 328 gm 189 328 lin 189 331 gm 189 364 lin 189 367 gm 189 367 lin 189 365 gm 189 365 lin 189 368 gm 189 400 lin 189 403 gm 189 403 lin 189 401 gm 189 401 lin 189 404 gm 189 487 lin 189 490 gm 189 490 lin 189 488 gm 189 488 lin 189 491 gm 189 524 lin 189 527 gm 189 527 lin 189 525 gm 189 525 lin 190 80 gm 203 80 lin 190 82 gm 203 82 lin 190 132 gm 203 132 lin 190 134 gm 203 134 lin 190 183 gm 203 183 lin 190 185 gm 203 185 lin 190 254 gm 203 254 lin 190 256 gm 203 256 lin 190 291 gm 203 291 lin 190 293 gm 203 293 lin 190 328 gm 203 328 lin 190 330 gm 203 330 lin 190 365 gm 203 365 lin 190 367 gm 203 367 lin 190 401 gm 203 401 lin 190 403 gm 203 403 lin 190 488 gm 203 488 lin 190 490 gm 203 490 lin 190 525 gm 203 525 lin 190 527 gm 203 527 lin 216 103 gm F 1 setTxMode (11)show 216 149 gm (1280)show 216 203 gm (6726213)show 216 265 gm (5.27)show 216 302 gm (0.48)show 216 339 gm (0.74)show 216 376 gm (0.48)show 216 436 gm (5255)show 216 499 gm (7.82)show 204 82 gm 0 gr 204 82 lin 204 80 gm 204 80 lin 204 83 gm 204 131 lin 204 134 gm 204 134 lin 204 132 gm 204 132 lin 204 135 gm 204 182 lin 204 185 gm 204 185 lin 204 183 gm 204 183 lin 204 186 gm 204 253 lin 204 256 gm 204 256 lin 204 254 gm 204 254 lin 204 257 gm 204 290 lin 204 293 gm 204 293 lin 204 291 gm 204 291 lin 204 294 gm 204 327 lin 204 330 gm 204 330 lin 204 328 gm 204 328 lin 204 331 gm 204 364 lin 204 367 gm 204 367 lin 204 365 gm 204 365 lin 204 368 gm 204 400 lin 204 403 gm 204 403 lin 204 401 gm 204 401 lin 204 404 gm 204 487 lin 204 490 gm 204 490 lin 204 488 gm 204 488 lin 204 491 gm 204 524 lin 204 527 gm 204 527 lin 204 525 gm 204 525 lin 205 80 gm 218 80 lin 205 82 gm 218 82 lin 221 80 gm 221 82 lin 219 80 gm 221 80 lin 219 82 gm 219 82 lin 219 82 lin 219 83 gm 219 131 lin 221 83 gm 221 131 lin 205 132 gm 218 132 lin 205 134 gm 218 134 lin 219 132 gm 219 134 lin 221 132 gm 221 134 lin 219 135 gm 219 182 lin 221 135 gm 221 182 lin 205 183 gm 218 183 lin 205 185 gm 218 185 lin 219 183 gm 219 185 lin 221 183 gm 221 185 lin 219 186 gm 219 253 lin 221 186 gm 221 253 lin 205 254 gm 218 254 lin 205 256 gm 218 256 lin 219 254 gm 219 256 lin 221 254 gm 221 256 lin 219 257 gm 219 290 lin 221 257 gm 221 290 lin 205 291 gm 218 291 lin 205 293 gm 218 293 lin 219 291 gm 219 293 lin 221 291 gm 221 293 lin 219 294 gm 219 327 lin 221 294 gm 221 327 lin 205 328 gm 218 328 lin 205 330 gm 218 330 lin 219 328 gm 219 330 lin 221 328 gm 221 330 lin 219 331 gm 219 364 lin 221 331 gm 221 364 lin 205 365 gm 218 365 lin 205 367 gm 218 367 lin 219 365 gm 219 367 lin 221 365 gm 221 367 lin 219 368 gm 219 400 lin 221 368 gm 221 400 lin 205 401 gm 218 401 lin 205 403 gm 218 403 lin 219 401 gm 219 403 lin 221 401 gm 221 403 lin 219 404 gm 219 487 lin 221 404 gm 221 487 lin 205 488 gm 218 488 lin 205 490 gm 218 490 lin 219 488 gm 219 490 lin 221 488 gm 221 490 lin 219 491 gm 219 524 lin 221 491 gm 221 524 lin 205 525 gm 218 525 lin 205 527 gm 218 527 lin 221 525 gm 221 527 lin 219 527 gm 221 527 lin 219 525 gm 219 525 lin 219 525 lin 233 79 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (Fig.11)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( )show 2 fs bu fc 2 F /|______Times-Italic fnt bn (Score sharing)show 249 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 1.28097 0. 32 0.12809 0.(This table shows that we have achieved the goal of reducing search overhead SO \(62% with 9)awidthshow 264 79 gm 0.64041 0. 32 0.06404 0.(processors\); the speedup with 11 processors was improved of 42% \(3.69 )awidthshow bu fc 2 F /|______Symbol fnt bn 0.38940 0.(\256)ashow bu fc 2 F /|______Times-Roman fnt bn 0.52368 0. 32 0.05236 0.( 5.27\). Values for F)awidthshow 264 511 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (pm)show 276 79 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.95855 0. 32 0.09585 0.(are approximated: they do not take in account overhead due to updating the local score. We can)awidthshow 287 79 gm (evaluate such an overhead as follows:)show 298 79 gm 0.60348 0. 32 0.06034 0.(\245\312with P processors, let Fpmr be the real production factor and OC due to score sharing; we have)awidthshow 309 79 gm (that:)show 0 0 pen 359 337 gm (nc 313 164 359 337 6 rc)kp 0 gr 359 337 lin psb currentpoint pse 313 164 gm 313 164 lin psb 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 5536 div 1472 3 -1 roll exch div scale currentpoint translate 64 52 translate -18 523 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Helvetica f1 (S) show 238 523 moveto 224 ns (VR) show 663 523 moveto 384 /Symbol f1 (=) show 963 523 moveto 384 /Helvetica f1 (P) show 1269 523 moveto 384 /Symbol f1 (\327) show 1395 523 moveto 384 /Helvetica f1 (F) show 1629 523 moveto 224 ns (pmr) show 2121 523 moveto 384 /Symbol f1 (\336) show 2581 523 moveto 384 /Helvetica f1 (F) show 2815 523 moveto 224 ns (pmr) show 3305 523 moveto 384 ns (=) show 3652 284 moveto (S) show 3908 284 moveto 224 ns (VR) show 3804 816 moveto 384 ns (P) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 3638 424 moveto 603 0 rlineto stroke -34 1313 moveto (F) show 200 1313 moveto 224 ns (pm) show 618 1313 moveto 384 /Symbol f1 (=) show 918 1313 moveto 384 /Helvetica f1 (F) show 1152 1313 moveto 224 ns (pmr) show 1626 1313 moveto 384 /Symbol f1 (+) show 1914 1313 moveto 384 /Helvetica f1 (OC) show 2582 1313 moveto 384 /Symbol f1 (\336) show 3062 1313 moveto 384 /Helvetica f1 (OC) show 3728 1313 moveto (=) show 4027 1313 moveto (F) show 4261 1313 moveto 224 ns (pm) show 4634 1313 moveto 384 ns (-) show 4805 1313 moveto (F) show 5039 1313 moveto 224 ns (pmr) show end pse 1 1 pen 368 79 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode (\245 in particular, with 11 processors:)show 0 0 pen 418 372 gm (nc 372 164 418 372 6 rc)kp 0 gr 418 372 lin psb currentpoint pse 372 164 gm 372 164 lin psb 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 6656 div 1472 3 -1 roll exch div scale currentpoint translate 64 36 translate -34 523 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Helvetica f1 (F) show 200 523 moveto 224 ns (pmr) show 601 523 moveto 384 /Helvetica f1 (\() show 721 523 moveto 384 /Helvetica f1 (11) show 1101 523 moveto 384 /Helvetica f1 (\)) show 1323 523 moveto 384 /Symbol f1 (=) show 1671 284 moveto 384 /Helvetica f1 (S) show 1927 284 moveto 224 ns (VR) show 1823 816 moveto 384 ns (P) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1657 424 moveto 603 0 rlineto stroke 2384 523 moveto 384 /Symbol f1 (=) show 2733 284 moveto 384 /Helvetica f1 (7) show 2947 284 moveto 384 /Helvetica f1 (.) show 3086 284 moveto 384 /Helvetica f1 (82) show 2930 816 moveto (11) show 2718 424 moveto 809 0 rlineto stroke 3651 523 moveto 384 /Symbol f1 (=) show 3969 523 moveto 384 /Helvetica f1 (0) show 4178 523 moveto 384 /Helvetica f1 (.) show 4314 523 moveto 384 /Helvetica f1 (71) show -14 1313 moveto 384 /Helvetica f1 (OC) show 563 1313 moveto 384 /Helvetica f1 (\() show 683 1313 moveto 384 /Helvetica f1 (11) show 1063 1313 moveto 384 /Helvetica f1 (\)) show 1285 1313 moveto 384 /Symbol f1 (=) show 1585 1313 moveto 384 /Helvetica f1 (F) show 1819 1313 moveto 224 ns (pm) show 2205 1313 moveto 384 /Symbol f1 (-) show 2472 1313 moveto 384 /Helvetica f1 (F) show 2706 1313 moveto 224 ns (pmr) show 3211 1313 moveto 384 /Symbol f1 (=) show 3529 1313 moveto 384 /Helvetica f1 (0) show 3738 1313 moveto 384 /Helvetica f1 (.) show 3874 1313 moveto 384 /Helvetica f1 (74) show 4378 1313 moveto 384 /Symbol f1 (-) show 4663 1313 moveto 384 /Helvetica f1 (0) show 4872 1313 moveto 384 /Helvetica f1 (.) show 5008 1313 moveto 384 /Helvetica f1 (71) show 5478 1313 moveto 384 /Symbol f1 (=) show 5796 1313 moveto 384 /Helvetica f1 (0) show 6005 1313 moveto 384 /Helvetica f1 (.) show 6142 1313 moveto 384 /Helvetica f1 (03) show end pse 1 1 pen 427 79 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0.10513 0. 32 0.01051 0.(Communication overhead is not negligible, however the improvements in search overhead are worth)awidthshow 438 79 gm (such a price.)show 468 79 gm 1 fs 12 fz bu fc 2 F /|______Times-Bold fnt bn (4.3 PVSplit)show 481 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.94223 0. 32 0.09422 0.(We have tested PVSplit with iterative deepening \(INIT=2-plies and MAX=5-plies\) and top-level)awidthshow 492 79 gm 0.78674 0. 32 0.07867 0.(sorting; moreover, THRESOLD=3-plies. We have made two sets of experiments, with or without)awidthshow 503 79 gm (global score.)show 532 96 gm 1 fs 10 fz bu fc 2 F /|______Times-Bold fnt bn (procs)show 532 145 gm (T\312\(sec\))show 532 200 gm (N\312\(nodes\))show 532 271 gm (S)show 532 308 gm (E)show 532 338 gm (Fpm)show 532 378 gm (SO)show 532 416 gm (SS\312\(nodes/sec\))show 532 502 gm (Sss)show 518 80 gm 0 gr 518 82 lin 518 80 gm 520 80 lin 520 82 gm 520 82 lin 520 82 lin 518 83 gm 518 131 lin 520 83 gm 520 131 lin 518 132 gm 518 134 lin 520 132 gm 520 134 lin 518 135 gm 518 182 lin 520 135 gm 520 182 lin 518 183 gm 518 185 lin 520 183 gm 520 185 lin 518 186 gm 518 253 lin 520 186 gm 520 253 lin 518 254 gm 518 256 lin 520 254 gm 520 256 lin 518 257 gm 518 290 lin 520 257 gm 520 290 lin 518 291 gm 518 293 lin 520 291 gm 520 293 lin 518 294 gm 518 327 lin 520 294 gm 520 327 lin 518 328 gm 518 330 lin 520 328 gm 520 330 lin 518 331 gm 518 364 lin 520 331 gm 520 364 lin 518 365 gm 518 367 lin 520 365 gm 520 367 lin 518 368 gm 518 400 lin 520 368 gm 520 400 lin 518 401 gm 518 403 lin 520 401 gm 520 403 lin 518 404 gm 518 487 lin 520 404 gm 520 487 lin 518 488 gm 518 490 lin 520 488 gm 520 490 lin 518 491 gm 518 524 lin 520 491 gm 520 524 lin 518 525 gm 518 527 lin 520 527 lin 520 525 gm 520 525 lin 520 525 lin 521 80 gm 534 80 lin 521 82 gm 534 82 lin 521 132 gm 534 132 lin 521 134 gm 534 134 lin 521 183 gm 534 183 lin 521 185 gm 534 185 lin 521 254 gm 534 254 lin 521 256 gm 534 256 lin 521 291 gm 534 291 lin 521 293 gm 534 293 lin 521 328 gm 534 328 lin 521 330 gm 534 330 lin 521 365 gm 534 365 lin 521 367 gm 534 367 lin 521 401 gm 534 401 lin 521 403 gm 534 403 lin 521 488 gm 534 488 lin 521 490 gm 534 490 lin 521 525 gm 534 525 lin 521 527 gm 534 527 lin 549 105 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn (1)show 549 149 gm (6740)show 549 203 gm (4529971)show 549 269 gm (---)show 549 306 gm (---)show 549 343 gm (---)show 549 380 gm (---)show 549 439 gm (672)show 549 503 gm (---)show 535 82 gm 0 gr 537 82 lin 535 80 gm 537 80 lin 535 83 gm 535 131 lin 537 83 gm 537 131 lin 535 134 gm 535 134 lin 537 132 gm 537 132 lin 535 132 gm 535 132 lin 537 134 gm 537 134 lin 535 135 gm 535 182 lin 537 135 gm 537 182 lin 535 185 gm 535 185 lin 537 183 gm 537 183 lin 535 183 gm 535 183 lin 537 185 gm 537 185 lin 535 186 gm 535 253 lin 537 186 gm 537 253 lin 535 256 gm 535 256 lin 537 254 gm 537 254 lin 535 254 gm 535 254 lin 537 256 gm 537 256 lin 535 257 gm 535 290 lin 537 257 gm 537 290 lin 535 293 gm 535 293 lin 537 291 gm 537 291 lin 535 291 gm 535 291 lin 537 293 gm 537 293 lin 535 294 gm 535 327 lin 537 294 gm 537 327 lin 535 330 gm 535 330 lin 537 328 gm 537 328 lin 535 328 gm 535 328 lin 537 330 gm 537 330 lin 535 331 gm 535 364 lin 537 331 gm 537 364 lin 535 367 gm 535 367 lin 537 365 gm 537 365 lin 535 365 gm 535 365 lin 537 367 gm 537 367 lin 535 368 gm 535 400 lin 537 368 gm 537 400 lin 535 403 gm 535 403 lin 537 401 gm 537 401 lin 535 401 gm 535 401 lin 537 403 gm 537 403 lin 535 404 gm 535 487 lin 537 404 gm 537 487 lin 535 490 gm 535 490 lin 537 488 gm 537 488 lin 535 488 gm 535 488 lin 537 490 gm 537 490 lin 535 491 gm 535 524 lin 537 491 gm 537 524 lin 535 527 gm 537 527 lin 535 525 gm 537 525 lin 538 80 gm 551 80 lin 538 82 gm 551 82 lin 538 132 gm 551 132 lin 538 134 gm 551 134 lin 538 183 gm 551 183 lin 538 185 gm 551 185 lin 538 254 gm 551 254 lin 538 256 gm 551 256 lin 538 291 gm 551 291 lin 538 293 gm 551 293 lin 538 328 gm 551 328 lin 538 330 gm 551 330 lin 538 365 gm 551 365 lin 538 367 gm 551 367 lin 538 401 gm 551 401 lin 538 403 gm 551 403 lin 538 488 gm 551 488 lin 538 490 gm 551 490 lin 538 525 gm 551 525 lin 538 527 gm 551 527 lin 564 105 gm F 1 setTxMode (3)show 564 149 gm (2693)show 564 203 gm (4949981)show 564 265 gm (2.50)show 564 302 gm (0.83)show 564 339 gm (0.91)show 564 376 gm (0.09)show 564 436 gm (1838)show 564 499 gm (2.73)show 552 82 gm 0 gr 552 82 lin 552 80 gm 552 80 lin 552 83 gm 552 131 lin 552 134 gm 552 134 lin 552 132 gm 552 132 lin 552 135 gm 552 182 lin 552 185 gm 552 185 lin 552 183 gm 552 183 lin 552 186 gm 552 253 lin 552 256 gm 552 256 lin 552 254 gm 552 254 lin 552 257 gm 552 290 lin 552 293 gm 552 293 lin 552 291 gm 552 291 lin 552 294 gm 552 327 lin 552 330 gm 552 330 lin 552 328 gm 552 328 lin 552 331 gm 552 364 lin 552 367 gm 552 367 lin 552 365 gm 552 365 lin 552 368 gm 552 400 lin 552 403 gm 552 403 lin 552 401 gm 552 401 lin 552 404 gm 552 487 lin 552 490 gm 552 490 lin 552 488 gm 552 488 lin 552 491 gm 552 524 lin 552 527 gm 552 527 lin 552 525 gm 552 525 lin 553 80 gm 566 80 lin 553 82 gm 566 82 lin 553 132 gm 566 132 lin 553 134 gm 566 134 lin 553 183 gm 566 183 lin 553 185 gm 566 185 lin 553 254 gm 566 254 lin 553 256 gm 566 256 lin 553 291 gm 566 291 lin 553 293 gm 566 293 lin 553 328 gm 566 328 lin 553 330 gm 566 330 lin 553 365 gm 566 365 lin 553 367 gm 566 367 lin 553 401 gm 566 401 lin 553 403 gm 566 403 lin 553 488 gm 566 488 lin 553 490 gm 566 490 lin 553 525 gm 566 525 lin 553 527 gm 566 527 lin 579 105 gm F 1 setTxMode (5)show 579 149 gm (1931)show 579 203 gm (5349308)show 579 265 gm (3.49)show 579 302 gm (0.70)show 579 339 gm (0.82)show 579 376 gm (0.18)show 579 436 gm (2770)show 579 499 gm (4.12)show 567 82 gm 0 gr 567 82 lin 567 80 gm 567 80 lin 567 83 gm 567 131 lin 567 134 gm 567 134 lin 567 132 gm 567 132 lin 567 135 gm 567 182 lin 567 185 gm 567 185 lin 567 183 gm 567 183 lin 567 186 gm 567 253 lin 567 256 gm 567 256 lin 567 254 gm 567 254 lin 567 257 gm 567 290 lin 567 293 gm 567 293 lin 567 291 gm 567 291 lin 567 294 gm 567 327 lin 567 330 gm 567 330 lin 567 328 gm 567 328 lin 567 331 gm 567 364 lin 567 367 gm 567 367 lin 567 365 gm 567 365 lin 567 368 gm 567 400 lin 567 403 gm 567 403 lin 567 401 gm 567 401 lin 567 404 gm 567 487 lin 567 490 gm 567 490 lin 567 488 gm 567 488 lin 567 491 gm 567 524 lin 567 527 gm 567 527 lin 567 525 gm 567 525 lin 568 80 gm 581 80 lin 568 82 gm 581 82 lin 568 132 gm 581 132 lin 568 134 gm 581 134 lin 568 183 gm 581 183 lin 568 185 gm 581 185 lin 568 254 gm 581 254 lin 568 256 gm 581 256 lin 568 291 gm 581 291 lin 568 293 gm 581 293 lin 568 328 gm 581 328 lin 568 330 gm 581 330 lin 568 365 gm 581 365 lin 568 367 gm 581 367 lin 568 401 gm 581 401 lin 568 403 gm 581 403 lin 568 488 gm 581 488 lin 568 490 gm 581 490 lin 568 525 gm 581 525 lin 568 527 gm 581 527 lin 594 105 gm F 1 setTxMode (7)show 594 149 gm (1659)show 594 203 gm (5657469)show 594 265 gm (4.06)show 594 302 gm (0.58)show 594 339 gm (0.75)show 594 376 gm (0.25)show 594 436 gm (3410)show 594 499 gm (5.07)show 582 82 gm 0 gr 582 82 lin 582 80 gm 582 80 lin 582 83 gm 582 131 lin 582 134 gm 582 134 lin 582 132 gm 582 132 lin 582 135 gm 582 182 lin 582 185 gm 582 185 lin 582 183 gm 582 183 lin 582 186 gm 582 253 lin 582 256 gm 582 256 lin 582 254 gm 582 254 lin 582 257 gm 582 290 lin 582 293 gm 582 293 lin 582 291 gm 582 291 lin 582 294 gm 582 327 lin 582 330 gm 582 330 lin 582 328 gm 582 328 lin 582 331 gm 582 364 lin 582 367 gm 582 367 lin 582 365 gm 582 365 lin 582 368 gm 582 400 lin 582 403 gm 582 403 lin 582 401 gm 582 401 lin 582 404 gm 582 487 lin 582 490 gm 582 490 lin 582 488 gm 582 488 lin 582 491 gm 582 524 lin 582 527 gm 582 527 lin 582 525 gm 582 525 lin 583 80 gm 596 80 lin 583 82 gm 596 82 lin 583 132 gm 596 132 lin 583 134 gm 596 134 lin 583 183 gm 596 183 lin 583 185 gm 596 185 lin 583 254 gm 596 254 lin 583 256 gm 596 256 lin 583 291 gm 596 291 lin 583 293 gm 596 293 lin 583 328 gm 596 328 lin 583 330 gm 596 330 lin 583 365 gm 596 365 lin 583 367 gm 596 367 lin 583 401 gm 596 401 lin 583 403 gm 596 403 lin 583 488 gm 596 488 lin 583 490 gm 596 490 lin 583 525 gm 596 525 lin 583 527 gm 596 527 lin 609 105 gm F 1 setTxMode (9)show 609 149 gm (1502)show 609 203 gm (6130143)show 609 265 gm (4.49)show 609 302 gm (0.50)show 609 339 gm (0.67)show 609 376 gm (0.35)show 609 436 gm (4081)show 609 499 gm (6.07)show 597 82 gm 0 gr 597 82 lin 597 80 gm 597 80 lin 597 83 gm 597 131 lin 597 134 gm 597 134 lin 597 132 gm 597 132 lin 597 135 gm 597 182 lin 597 185 gm 597 185 lin 597 183 gm 597 183 lin 597 186 gm 597 253 lin 597 256 gm 597 256 lin 597 254 gm 597 254 lin 597 257 gm 597 290 lin 597 293 gm 597 293 lin 597 291 gm 597 291 lin 597 294 gm 597 327 lin 597 330 gm 597 330 lin 597 328 gm 597 328 lin 597 331 gm 597 364 lin 597 367 gm 597 367 lin 597 365 gm 597 365 lin 597 368 gm 597 400 lin 597 403 gm 597 403 lin 597 401 gm 597 401 lin 597 404 gm 597 487 lin 597 490 gm 597 490 lin 597 488 gm 597 488 lin 597 491 gm 597 524 lin 597 527 gm 597 527 lin 597 525 gm 597 525 lin 598 80 gm 611 80 lin 598 82 gm 611 82 lin 598 132 gm 611 132 lin 598 134 gm 611 134 lin 598 183 gm 611 183 lin 598 185 gm 611 185 lin 598 254 gm 611 254 lin 598 256 gm 611 256 lin 598 291 gm 611 291 lin 598 293 gm 611 293 lin 598 328 gm 611 328 lin 598 330 gm 611 330 lin 598 365 gm 611 365 lin 598 367 gm 611 367 lin 598 401 gm 611 401 lin 598 403 gm 611 403 lin 598 488 gm 611 488 lin 598 490 gm 611 490 lin 598 525 gm 611 525 lin 598 527 gm 611 527 lin 624 103 gm F 1 setTxMode (11)show 624 149 gm (1446)show 624 203 gm (6445828)show 624 265 gm (4.66)show 624 302 gm (0.42)show 624 339 gm (0.60)show 624 376 gm (0.42)show 624 436 gm (4458)show 624 499 gm (6.63)show 612 82 gm 0 gr 612 82 lin 612 80 gm 612 80 lin 612 83 gm 612 131 lin 612 134 gm 612 134 lin 612 132 gm 612 132 lin 612 135 gm 612 182 lin 612 185 gm 612 185 lin 612 183 gm 612 183 lin 612 186 gm 612 253 lin 612 256 gm 612 256 lin 612 254 gm 612 254 lin 612 257 gm 612 290 lin 612 293 gm 612 293 lin 612 291 gm 612 291 lin 612 294 gm 612 327 lin 612 330 gm 612 330 lin 612 328 gm 612 328 lin 612 331 gm 612 364 lin 612 367 gm 612 367 lin 612 365 gm 612 365 lin 612 368 gm 612 400 lin 612 403 gm 612 403 lin 612 401 gm 612 401 lin 612 404 gm 612 487 lin 612 490 gm 612 490 lin 612 488 gm 612 488 lin 612 491 gm 612 524 lin 612 527 gm 612 527 lin 612 525 gm 612 525 lin 613 80 gm 626 80 lin 613 82 gm 626 82 lin 629 80 gm 629 82 lin 627 80 gm 629 80 lin 627 82 gm 627 82 lin 627 82 lin 627 83 gm 627 131 lin 629 83 gm 629 131 lin 613 132 gm 626 132 lin 613 134 gm 626 134 lin 627 132 gm 627 134 lin 629 132 gm 629 134 lin 627 135 gm 627 182 lin 629 135 gm 629 182 lin 613 183 gm 626 183 lin 613 185 gm 626 185 lin 627 183 gm 627 185 lin 629 183 gm 629 185 lin 627 186 gm 627 253 lin 629 186 gm 629 253 lin 613 254 gm 626 254 lin 613 256 gm 626 256 lin 627 254 gm 627 256 lin 629 254 gm 629 256 lin 627 257 gm 627 290 lin 629 257 gm 629 290 lin 613 291 gm 626 291 lin 613 293 gm 626 293 lin 627 291 gm 627 293 lin 629 291 gm 629 293 lin 627 294 gm 627 327 lin 629 294 gm 629 327 lin 613 328 gm 626 328 lin 613 330 gm 626 330 lin 627 328 gm 627 330 lin 629 328 gm 629 330 lin 627 331 gm 627 364 lin 629 331 gm 629 364 lin 613 365 gm 626 365 lin 613 367 gm 626 367 lin 627 365 gm 627 367 lin 629 365 gm 629 367 lin 627 368 gm 627 400 lin 629 368 gm 629 400 lin 613 401 gm 626 401 lin 613 403 gm 626 403 lin 627 401 gm 627 403 lin 629 401 gm 629 403 lin 627 404 gm 627 487 lin 629 404 gm 629 487 lin 613 488 gm 626 488 lin 613 490 gm 626 490 lin 627 488 gm 627 490 lin 629 488 gm 629 490 lin 627 491 gm 627 524 lin 629 491 gm 629 524 lin 613 525 gm 626 525 lin 613 527 gm 626 527 lin 629 525 gm 629 527 lin 627 527 gm 629 527 lin 627 525 gm 627 525 lin 627 525 lin 641 79 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (Fig. 12 )show 2 fs bu fc 2 F /|______Times-Italic fnt bn (PVSplit without score sharing)show 657 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.10940 0. 32 0.01094 0.(PVSplit reduces search overhead with respect to score sharing \(see Fig.11\), however its efficiency is)awidthshow 668 79 gm 0.78536 0. 32 0.07853 0.(lower. Compare the production factors: PVSplit gives very low values \(14% with 11 processors\).)awidthshow 679 79 gm 0.79605 0. 32 0.07960 0.(The reason is the synchronization necessary along the principal variation; we can reduce such an)awidthshow 690 79 gm (overhead with a more balanced load distribution.)show 701 79 gm 0.02395 0. 32 0.00239 0.(We also have to take into account the fixed cost of each splitting: communication overhead has to be)awidthshow 712 79 gm (multiplied for each node in the principal variation that is used for parallel splitting.)show F T cp %%Page: ? 13 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 336 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Helvetica fnt bn (A Comparison of Parallel Search Algorithms)show 773 79 gm (UBLCS-94-14)show 773 514 gm (11)show 124 96 gm 1 fs bu fc 2 F /|______Times-Bold fnt bn (Procs)show 124 145 gm (T\312\(sec\))show 124 200 gm (N\312\(nodes\))show 124 271 gm (S)show 124 308 gm (E)show 124 338 gm (Fpm)show 124 378 gm (SO)show 124 416 gm (SS\312\(nodes/sec\))show 124 502 gm (Sss)show 110 80 gm 0 gr 110 82 lin 110 80 gm 112 80 lin 112 82 gm 112 82 lin 112 82 lin 110 83 gm 110 131 lin 112 83 gm 112 131 lin 110 132 gm 110 134 lin 112 132 gm 112 134 lin 110 135 gm 110 182 lin 112 135 gm 112 182 lin 110 183 gm 110 185 lin 112 183 gm 112 185 lin 110 186 gm 110 253 lin 112 186 gm 112 253 lin 110 254 gm 110 256 lin 112 254 gm 112 256 lin 110 257 gm 110 290 lin 112 257 gm 112 290 lin 110 291 gm 110 293 lin 112 291 gm 112 293 lin 110 294 gm 110 327 lin 112 294 gm 112 327 lin 110 328 gm 110 330 lin 112 328 gm 112 330 lin 110 331 gm 110 364 lin 112 331 gm 112 364 lin 110 365 gm 110 367 lin 112 365 gm 112 367 lin 110 368 gm 110 400 lin 112 368 gm 112 400 lin 110 401 gm 110 403 lin 112 401 gm 112 403 lin 110 404 gm 110 487 lin 112 404 gm 112 487 lin 110 488 gm 110 490 lin 112 488 gm 112 490 lin 110 491 gm 110 524 lin 112 491 gm 112 524 lin 110 525 gm 110 527 lin 112 527 lin 112 525 gm 112 525 lin 112 525 lin 113 80 gm 126 80 lin 113 82 gm 126 82 lin 113 132 gm 126 132 lin 113 134 gm 126 134 lin 113 183 gm 126 183 lin 113 185 gm 126 185 lin 113 254 gm 126 254 lin 113 256 gm 126 256 lin 113 291 gm 126 291 lin 113 293 gm 126 293 lin 113 328 gm 126 328 lin 113 330 gm 126 330 lin 113 365 gm 126 365 lin 113 367 gm 126 367 lin 113 401 gm 126 401 lin 113 403 gm 126 403 lin 113 488 gm 126 488 lin 113 490 gm 126 490 lin 113 525 gm 126 525 lin 113 527 gm 126 527 lin 141 105 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn (1)show 141 149 gm (6740)show 141 203 gm (4529971)show 141 269 gm (---)show 141 306 gm (---)show 141 343 gm (---)show 141 380 gm (---)show 141 439 gm (672)show 141 503 gm (---)show 127 82 gm 0 gr 129 82 lin 127 80 gm 129 80 lin 127 83 gm 127 131 lin 129 83 gm 129 131 lin 127 134 gm 127 134 lin 129 132 gm 129 132 lin 127 132 gm 127 132 lin 129 134 gm 129 134 lin 127 135 gm 127 182 lin 129 135 gm 129 182 lin 127 185 gm 127 185 lin 129 183 gm 129 183 lin 127 183 gm 127 183 lin 129 185 gm 129 185 lin 127 186 gm 127 253 lin 129 186 gm 129 253 lin 127 256 gm 127 256 lin 129 254 gm 129 254 lin 127 254 gm 127 254 lin 129 256 gm 129 256 lin 127 257 gm 127 290 lin 129 257 gm 129 290 lin 127 293 gm 127 293 lin 129 291 gm 129 291 lin 127 291 gm 127 291 lin 129 293 gm 129 293 lin 127 294 gm 127 327 lin 129 294 gm 129 327 lin 127 330 gm 127 330 lin 129 328 gm 129 328 lin 127 328 gm 127 328 lin 129 330 gm 129 330 lin 127 331 gm 127 364 lin 129 331 gm 129 364 lin 127 367 gm 127 367 lin 129 365 gm 129 365 lin 127 365 gm 127 365 lin 129 367 gm 129 367 lin 127 368 gm 127 400 lin 129 368 gm 129 400 lin 127 403 gm 127 403 lin 129 401 gm 129 401 lin 127 401 gm 127 401 lin 129 403 gm 129 403 lin 127 404 gm 127 487 lin 129 404 gm 129 487 lin 127 490 gm 127 490 lin 129 488 gm 129 488 lin 127 488 gm 127 488 lin 129 490 gm 129 490 lin 127 491 gm 127 524 lin 129 491 gm 129 524 lin 127 527 gm 129 527 lin 127 525 gm 129 525 lin 130 80 gm 143 80 lin 130 82 gm 143 82 lin 130 132 gm 143 132 lin 130 134 gm 143 134 lin 130 183 gm 143 183 lin 130 185 gm 143 185 lin 130 254 gm 143 254 lin 130 256 gm 143 256 lin 130 291 gm 143 291 lin 130 293 gm 143 293 lin 130 328 gm 143 328 lin 130 330 gm 143 330 lin 130 365 gm 143 365 lin 130 367 gm 143 367 lin 130 401 gm 143 401 lin 130 403 gm 143 403 lin 130 488 gm 143 488 lin 130 490 gm 143 490 lin 130 525 gm 143 525 lin 130 527 gm 143 527 lin 156 105 gm F 1 setTxMode (3)show 156 149 gm (2640)show 156 203 gm (4770665)show 156 265 gm (2.55)show 156 302 gm (0.85)show 156 339 gm (0.91)show 156 376 gm (0.05)show 156 436 gm (1807)show 156 499 gm (2.69)show 144 82 gm 0 gr 144 82 lin 144 80 gm 144 80 lin 144 83 gm 144 131 lin 144 134 gm 144 134 lin 144 132 gm 144 132 lin 144 135 gm 144 182 lin 144 185 gm 144 185 lin 144 183 gm 144 183 lin 144 186 gm 144 253 lin 144 256 gm 144 256 lin 144 254 gm 144 254 lin 144 257 gm 144 290 lin 144 293 gm 144 293 lin 144 291 gm 144 291 lin 144 294 gm 144 327 lin 144 330 gm 144 330 lin 144 328 gm 144 328 lin 144 331 gm 144 364 lin 144 367 gm 144 367 lin 144 365 gm 144 365 lin 144 368 gm 144 400 lin 144 403 gm 144 403 lin 144 401 gm 144 401 lin 144 404 gm 144 487 lin 144 490 gm 144 490 lin 144 488 gm 144 488 lin 144 491 gm 144 524 lin 144 527 gm 144 527 lin 144 525 gm 144 525 lin 145 80 gm 158 80 lin 145 82 gm 158 82 lin 145 132 gm 158 132 lin 145 134 gm 158 134 lin 145 183 gm 158 183 lin 145 185 gm 158 185 lin 145 254 gm 158 254 lin 145 256 gm 158 256 lin 145 291 gm 158 291 lin 145 293 gm 158 293 lin 145 328 gm 158 328 lin 145 330 gm 158 330 lin 145 365 gm 158 365 lin 145 367 gm 158 367 lin 145 401 gm 158 401 lin 145 403 gm 158 403 lin 145 488 gm 158 488 lin 145 490 gm 158 490 lin 145 525 gm 158 525 lin 145 527 gm 158 527 lin 171 105 gm F 1 setTxMode (5)show 171 149 gm (1797)show 171 203 gm (5020905)show 171 265 gm (3.75)show 171 302 gm (0.75)show 171 339 gm (0.84)show 171 376 gm (0.11)show 171 436 gm (2794)show 171 499 gm (4.16)show 159 82 gm 0 gr 159 82 lin 159 80 gm 159 80 lin 159 83 gm 159 131 lin 159 134 gm 159 134 lin 159 132 gm 159 132 lin 159 135 gm 159 182 lin 159 185 gm 159 185 lin 159 183 gm 159 183 lin 159 186 gm 159 253 lin 159 256 gm 159 256 lin 159 254 gm 159 254 lin 159 257 gm 159 290 lin 159 293 gm 159 293 lin 159 291 gm 159 291 lin 159 294 gm 159 327 lin 159 330 gm 159 330 lin 159 328 gm 159 328 lin 159 331 gm 159 364 lin 159 367 gm 159 367 lin 159 365 gm 159 365 lin 159 368 gm 159 400 lin 159 403 gm 159 403 lin 159 401 gm 159 401 lin 159 404 gm 159 487 lin 159 490 gm 159 490 lin 159 488 gm 159 488 lin 159 491 gm 159 524 lin 159 527 gm 159 527 lin 159 525 gm 159 525 lin 160 80 gm 173 80 lin 160 82 gm 173 82 lin 160 132 gm 173 132 lin 160 134 gm 173 134 lin 160 183 gm 173 183 lin 160 185 gm 173 185 lin 160 254 gm 173 254 lin 160 256 gm 173 256 lin 160 291 gm 173 291 lin 160 293 gm 173 293 lin 160 328 gm 173 328 lin 160 330 gm 173 330 lin 160 365 gm 173 365 lin 160 367 gm 173 367 lin 160 401 gm 173 401 lin 160 403 gm 173 403 lin 160 488 gm 173 488 lin 160 490 gm 173 490 lin 160 525 gm 173 525 lin 160 527 gm 173 527 lin 186 105 gm F 1 setTxMode (7)show 186 149 gm (1443)show 186 203 gm (5228542)show 186 265 gm (4.67)show 186 302 gm (0.67)show 186 339 gm (0.77)show 186 376 gm (0.15)show 186 436 gm (3623)show 186 499 gm (5.39)show 174 82 gm 0 gr 174 82 lin 174 80 gm 174 80 lin 174 83 gm 174 131 lin 174 134 gm 174 134 lin 174 132 gm 174 132 lin 174 135 gm 174 182 lin 174 185 gm 174 185 lin 174 183 gm 174 183 lin 174 186 gm 174 253 lin 174 256 gm 174 256 lin 174 254 gm 174 254 lin 174 257 gm 174 290 lin 174 293 gm 174 293 lin 174 291 gm 174 291 lin 174 294 gm 174 327 lin 174 330 gm 174 330 lin 174 328 gm 174 328 lin 174 331 gm 174 364 lin 174 367 gm 174 367 lin 174 365 gm 174 365 lin 174 368 gm 174 400 lin 174 403 gm 174 403 lin 174 401 gm 174 401 lin 174 404 gm 174 487 lin 174 490 gm 174 490 lin 174 488 gm 174 488 lin 174 491 gm 174 524 lin 174 527 gm 174 527 lin 174 525 gm 174 525 lin 175 80 gm 188 80 lin 175 82 gm 188 82 lin 175 132 gm 188 132 lin 175 134 gm 188 134 lin 175 183 gm 188 183 lin 175 185 gm 188 185 lin 175 254 gm 188 254 lin 175 256 gm 188 256 lin 175 291 gm 188 291 lin 175 293 gm 188 293 lin 175 328 gm 188 328 lin 175 330 gm 188 330 lin 175 365 gm 188 365 lin 175 367 gm 188 367 lin 175 401 gm 188 401 lin 175 403 gm 188 403 lin 175 488 gm 188 488 lin 175 490 gm 188 490 lin 175 525 gm 188 525 lin 175 527 gm 188 527 lin 201 105 gm F 1 setTxMode (9)show 201 149 gm (1255)show 201 203 gm (5358664)show 201 265 gm (5.37)show 201 302 gm (0.60)show 201 339 gm (0.71)show 201 376 gm (0.18)show 201 436 gm (4270)show 201 499 gm (6.35)show 189 82 gm 0 gr 189 82 lin 189 80 gm 189 80 lin 189 83 gm 189 131 lin 189 134 gm 189 134 lin 189 132 gm 189 132 lin 189 135 gm 189 182 lin 189 185 gm 189 185 lin 189 183 gm 189 183 lin 189 186 gm 189 253 lin 189 256 gm 189 256 lin 189 254 gm 189 254 lin 189 257 gm 189 290 lin 189 293 gm 189 293 lin 189 291 gm 189 291 lin 189 294 gm 189 327 lin 189 330 gm 189 330 lin 189 328 gm 189 328 lin 189 331 gm 189 364 lin 189 367 gm 189 367 lin 189 365 gm 189 365 lin 189 368 gm 189 400 lin 189 403 gm 189 403 lin 189 401 gm 189 401 lin 189 404 gm 189 487 lin 189 490 gm 189 490 lin 189 488 gm 189 488 lin 189 491 gm 189 524 lin 189 527 gm 189 527 lin 189 525 gm 189 525 lin 190 80 gm 203 80 lin 190 82 gm 203 82 lin 190 132 gm 203 132 lin 190 134 gm 203 134 lin 190 183 gm 203 183 lin 190 185 gm 203 185 lin 190 254 gm 203 254 lin 190 256 gm 203 256 lin 190 291 gm 203 291 lin 190 293 gm 203 293 lin 190 328 gm 203 328 lin 190 330 gm 203 330 lin 190 365 gm 203 365 lin 190 367 gm 203 367 lin 190 401 gm 203 401 lin 190 403 gm 203 403 lin 190 488 gm 203 488 lin 190 490 gm 203 490 lin 190 525 gm 203 525 lin 190 527 gm 203 527 lin 216 103 gm F 1 setTxMode (11)show 216 149 gm (1210)show 216 203 gm (5704328)show 216 265 gm (5.57)show 216 302 gm (0.51)show 216 339 gm (0.64)show 216 376 gm (0.26)show 216 436 gm (4714)show 216 499 gm (7.01)show 204 82 gm 0 gr 204 82 lin 204 80 gm 204 80 lin 204 83 gm 204 131 lin 204 134 gm 204 134 lin 204 132 gm 204 132 lin 204 135 gm 204 182 lin 204 185 gm 204 185 lin 204 183 gm 204 183 lin 204 186 gm 204 253 lin 204 256 gm 204 256 lin 204 254 gm 204 254 lin 204 257 gm 204 290 lin 204 293 gm 204 293 lin 204 291 gm 204 291 lin 204 294 gm 204 327 lin 204 330 gm 204 330 lin 204 328 gm 204 328 lin 204 331 gm 204 364 lin 204 367 gm 204 367 lin 204 365 gm 204 365 lin 204 368 gm 204 400 lin 204 403 gm 204 403 lin 204 401 gm 204 401 lin 204 404 gm 204 487 lin 204 490 gm 204 490 lin 204 488 gm 204 488 lin 204 491 gm 204 524 lin 204 527 gm 204 527 lin 204 525 gm 204 525 lin 205 80 gm 218 80 lin 205 82 gm 218 82 lin 221 80 gm 221 82 lin 219 80 gm 221 80 lin 219 82 gm 219 82 lin 219 82 lin 219 83 gm 219 131 lin 221 83 gm 221 131 lin 205 132 gm 218 132 lin 205 134 gm 218 134 lin 219 132 gm 219 134 lin 221 132 gm 221 134 lin 219 135 gm 219 182 lin 221 135 gm 221 182 lin 205 183 gm 218 183 lin 205 185 gm 218 185 lin 219 183 gm 219 185 lin 221 183 gm 221 185 lin 219 186 gm 219 253 lin 221 186 gm 221 253 lin 205 254 gm 218 254 lin 205 256 gm 218 256 lin 219 254 gm 219 256 lin 221 254 gm 221 256 lin 219 257 gm 219 290 lin 221 257 gm 221 290 lin 205 291 gm 218 291 lin 205 293 gm 218 293 lin 219 291 gm 219 293 lin 221 291 gm 221 293 lin 219 294 gm 219 327 lin 221 294 gm 221 327 lin 205 328 gm 218 328 lin 205 330 gm 218 330 lin 219 328 gm 219 330 lin 221 328 gm 221 330 lin 219 331 gm 219 364 lin 221 331 gm 221 364 lin 205 365 gm 218 365 lin 205 367 gm 218 367 lin 219 365 gm 219 367 lin 221 365 gm 221 367 lin 219 368 gm 219 400 lin 221 368 gm 221 400 lin 205 401 gm 218 401 lin 205 403 gm 218 403 lin 219 401 gm 219 403 lin 221 401 gm 221 403 lin 219 404 gm 219 487 lin 221 404 gm 221 487 lin 205 488 gm 218 488 lin 205 490 gm 218 490 lin 219 488 gm 219 490 lin 221 488 gm 221 490 lin 219 491 gm 219 524 lin 221 491 gm 221 524 lin 205 525 gm 218 525 lin 205 527 gm 218 527 lin 221 525 gm 221 527 lin 219 527 gm 221 527 lin 219 525 gm 219 525 lin 219 525 lin 233 79 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (Fig.13)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( )show 2 fs bu fc 2 F /|______Times-Italic fnt bn (PVSplit with score sharing)show 249 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.65200 0. 32 0.06520 0.(Applying score sharing to PVSplit we reduce search overhead without loss \(Fig.13\): in fact, these)awidthshow 260 79 gm (heuristics handle different parts of the game tree:)show 272 88 gm (\245\312PVSplit is used in search of subtrees 2..P \(if we use P processors\))show 285 88 gm (\245\312score sharing is used for subtrees after the Pth subtree.)show 297 79 gm 0.34881 0. 32 0.03488 0.(This algorithm gives the best speedups among those we have tested. We remark that there is a high)awidthshow 308 79 gm (synchronization overhead caused by nodes along the principal variation.)show 338 79 gm 1 fs 12 fz bu fc 2 F /|______Times-Bold fnt bn (5. Dynamic splitting)show 351 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.84838 0. 32 0.08483 0.(The main problem with static splitting is load distribution. The master-worker model is based on)awidthshow 362 79 gm 0.72189 0. 32 0.07218 0.(sequential jobs that are perfomed without attempting to parallelize them and are assigned without)awidthshow 377 79 gm 1.80435 0. 32 0.18043 0.(estimating the computational costs. Since for parallel )awidthshow 377 337 gm bu fc 2 F /|______Symbol fnt bn 0.74351 0.(ab)ashow bu fc 2 F /|______Times-Roman fnt bn 1.89697 0. 32 0.18969 0.( we cannot schedule jobs aiming at)awidthshow 389 79 gm (minimizing idle times, there is no way of dynamically balancing the load.)show 419 79 gm 1 fs 12 fz bu fc 2 F /|______Times-Bold fnt bn (5.1 Dynamic job allocation)show 432 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.39657 0. 32 0.03965 0.(A first solution to this problem consists of avoiding \322atomic\323 sequential jobs. We defined a variant)awidthshow 443 79 gm 0.75973 0. 32 0.07597 0.(of the core algorithm in which when there are no more jobs in the agenda the workers that finish)awidthshow 454 79 gm 0.38314 0. 32 0.03831 0.(their jobs help the busy ones. This means that a busy worker accepts help and splits its search tree,)awidthshow 465 79 gm 0.56610 0. 32 0.05661 0.(becoming a supervisor. We will apply this idea only to children of the root node. Since we cannot)awidthshow 476 79 gm 0.63034 0. 32 0.06303 0.(forecast how long the evaluation of a subtree will take, nor which nodes will be assigned to other)awidthshow 487 79 gm (processors, we classify this a dynamic splitting algorithm.)show 498 79 gm 1.57165 0. 32 0.15716 0.(There are several choice to implement cooperation among workers: we have implemented the)awidthshow 509 79 gm (following one.)show 521 88 gm 1.35116 0. 32 0.13511 0.(\245\312An explorer E)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.20555 0.(f)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 1.13021 0. 32 0.11302 0.( completes a search job and finds an empty agenda; however, there are other)awidthshow 532 101 gm (workers still busy. E)show 532 191 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (f)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( notifies to be free to a busy worker E)show 532 359 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (r)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( ;)show 545 88 gm (\245\312E)show 545 101 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (r)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( decomposes its subtree S, and sends tasks to free explorers;)show 557 79 gm (Processes that cooperate to the search are dynamically partitioned in three sets:)show 569 88 gm (\245\312set F of processes that completed their tasks and become free;)show 582 88 gm (\245\312set R)show 9 fz bu fc 2 F /|______Times-Roman fnt bn (p)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( of processes that distribute their subtrees;)show 595 88 gm (\245\312set R)show 9 fz bu fc 2 F /|______Times-Roman fnt bn (s)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( of processes that sequentially evaluate their subtrees.)show F T cp %%Page: ? 14 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 336 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Helvetica fnt bn (A Comparison of Parallel Search Algorithms)show 773 79 gm (UBLCS-94-14)show 773 514 gm (12)show 781 538 734 505 th 158 243 gm tu (nc 110 104 505 499 6 rc)kp ts 9 fz bu fc 2 F /|______Helvetica fnt bn (P1)show tu ts 157 270 gm (P2)show tu ts 158 297 gm (P3)show tu ts 158 322 gm (P4)show tu 0 gr 146.5 238.5 163.5 256.5 0 rc 146.5 266.5 163.5 284.5 0 rc 146.5 293.5 163.5 310.5 0 rc 146.5 318.5 163.5 335.5 0 rc ts 238 253 gm F 1 setTxMode (P1)show tu ts 237 279 gm (P2)show tu ts 238 306 gm (P4)show tu ts 281 279 gm (P3)show tu 0 gr 226.5 248.5 243.5 266.5 0 rc 226.5 275.5 243.5 293.5 0 rc 226.5 302.5 243.5 319.5 0 rc 269.5 275.5 286.5 292.5 0 rc 244 284 gm 269 284 lin ts 346 260 gm F 1 setTxMode (P1)show tu ts 345 295 gm (P4)show tu ts 391 258 gm (P2)show tu 0 gr 334.5 255.5 352.5 272.5 0 rc 334.5 291.5 351.5 309.5 0 rc 379.5 254.5 396.5 272.5 0 rc ts 390 295 gm F 1 setTxMode (P3)show tu 0 gr 378.5 291.5 396.5 308.5 0 rc 352 263 gm 378 263 lin ts 147 361 gm F 1 setTxMode (Rs={P1,P2,P3,P4})show 157 361 gm (Rp=)show 167 361 gm (F=)show tu ts 250 372 gm (Rs={P1,P4})show 260 372 gm (Rp={P2})show 271 372 gm (F={P3})show tu 352 263 gm 0 gr 378 300 lin ts 356 374 gm F 1 setTxMode (Rs={P4})show 367 374 gm (Rp={P1})show 377 374 gm (F={P2,P3})show tu ts 465 371 gm (Rs=)show 475 371 gm (Rp={P4})show 485 371 gm (F={P1,P2,P3})show tu 0 gr 136.5 358.5 174.5 431.5 0 rc 239.5 358.5 276.5 431.5 0 rc 347.5 358.5 385.5 431.5 0 rc 453.5 358.5 491.5 431.5 0 rc ts 498 249 gm F 1 setTxMode (P1)show tu ts 497 276 gm (P2)show tu ts 498 302 gm (P3)show tu 0 gr 486.5 245.5 503.5 262.5 0 rc 486.5 272.5 503.5 289.5 0 rc 486.5 299.5 503.5 316.5 0 rc 459 280 gm 486 280 lin 459 281 gm 486 308 lin 459 280 gm 486 253 lin ts 453 276 gm F 1 setTxMode (P4)show tu 0 gr 442.5 271.5 459.5 288.5 0 rc pr 226 396 pl 216 392 pl 216 396 pl 216 398 pl 226 396 pl 4 ep 188 396 gm 216 396 lin pr 332 396 pl 323 392 pl 323 396 pl 323 398 pl 332 396 pl 4 ep 295 396 gm 323 396 lin pr 439 396 pl 430 392 pl 430 396 pl 430 398 pl 439 396 pl 4 ep 402 396 gm 430 396 lin ts 246 108 gm F 1 setTxMode (democratic cooperation)show 257 108 gm (at first level;)show 267 108 gm (master-worker)show 277 108 gm (with second level)show tu 0 gr 427.5 106.5 443.5 216.5 0 rc 239.5 106.5 290.5 206.5 0 rc 164.5 110.5 180.5 214.5 0 rc pr 159 229 pl 165 222 pl 162 221 pl 158 220 pl 159 229 pl 4 ep 164 212 gm 158 234 lin pr 259 247 pl 264 238 pl 260 238 pl 258 237 pl 259 247 pl 4 ep 266 207 gm 260 238 lin pr 332 242 pl 325 236 pl 323 238 pl 322 241 pl 332 242 pl 4 ep 265 207 gm 323 238 lin pr 458 245 pl 454 236 pl 451 238 pl 449 239 pl 458 245 pl 4 ep 434 216 gm 451 238 lin ts 175 112 gm F 1 setTxMode (democratic cooperation)show tu ts 465 386 gm bu fc 2 F /|______Symbol fnt bn (\306)show tu ts 167 371 gm (\306)show tu ts 158 377 gm (\306)show tu ts 194 405 gm bu fc 2 F /|______Helvetica fnt bn (P3 terminates a search)show 204 405 gm (and informs P2;)show 214 405 gm (P2 distributes a subtree)show tu ts 302 408 gm (P2 terminates;)show 312 408 gm (P1 distributes)show 323 408 gm (two subtrees)show tu ts 410 405 gm (P1 terminates;)show 420 405 gm (P4 distributes)show 431 405 gm (three subtrees)show tu ts 438 114 gm (pure master-worker)show tu 99 77 gm (nc 30 28 811 566 6 rc)kp 0 gr 99 525 lin 544 244 gm F 1 setTxMode 11 fz bu fc 2 F /|______Times-Roman fnt bn (Fig.14)show 1 fs bu fc 2 F /|______Times-Bold fnt bn ( Dynamic splitting)show 562 77 gm 0 gr 562 525 lin 581 79 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.55099 0. 32 0.05509 0.(In this way we put a limit to the splittings that can happen at run-time, that are expensive: at most)awidthshow 592 79 gm 0.97015 0. 32 0.09701 0.(they are #F. Thus, the algorithm executed by each worker on its own subtree amounts to classic)awidthshow 603 79 gm 0.13885 0. 32 0.01388 0.(alphabeta until another worker declares to be available to help, after that the master-worker model is)awidthshow 614 79 gm (used. The following table summarizes the results obtained with this algorithm.)show 643 96 gm 1 fs 10 fz bu fc 2 F /|______Times-Bold fnt bn (Procs)show 643 145 gm (T\312\(sec\))show 643 200 gm (N\312\(nodes\))show 643 271 gm (S)show 643 308 gm (E)show 643 338 gm (Fpm)show 643 378 gm (SO)show 643 416 gm (SS\312\(nodes/sec\))show 643 502 gm (Sss)show 629 80 gm 0 gr 629 82 lin 629 80 gm 631 80 lin 631 82 gm 631 82 lin 631 82 lin 629 83 gm 629 131 lin 631 83 gm 631 131 lin 629 132 gm 629 134 lin 631 132 gm 631 134 lin 629 135 gm 629 182 lin 631 135 gm 631 182 lin 629 183 gm 629 185 lin 631 183 gm 631 185 lin 629 186 gm 629 253 lin 631 186 gm 631 253 lin 629 254 gm 629 256 lin 631 254 gm 631 256 lin 629 257 gm 629 290 lin 631 257 gm 631 290 lin 629 291 gm 629 293 lin 631 291 gm 631 293 lin 629 294 gm 629 327 lin 631 294 gm 631 327 lin 629 328 gm 629 330 lin 631 328 gm 631 330 lin 629 331 gm 629 364 lin 631 331 gm 631 364 lin 629 365 gm 629 367 lin 631 365 gm 631 367 lin 629 368 gm 629 400 lin 631 368 gm 631 400 lin 629 401 gm 629 403 lin 631 401 gm 631 403 lin 629 404 gm 629 487 lin 631 404 gm 631 487 lin 629 488 gm 629 490 lin 631 488 gm 631 490 lin 629 491 gm 629 524 lin 631 491 gm 631 524 lin 629 525 gm 629 527 lin 631 527 lin 631 525 gm 631 525 lin 631 525 lin 632 80 gm 645 80 lin 632 82 gm 645 82 lin 632 132 gm 645 132 lin 632 134 gm 645 134 lin 632 183 gm 645 183 lin 632 185 gm 645 185 lin 632 254 gm 645 254 lin 632 256 gm 645 256 lin 632 291 gm 645 291 lin 632 293 gm 645 293 lin 632 328 gm 645 328 lin 632 330 gm 645 330 lin 632 365 gm 645 365 lin 632 367 gm 645 367 lin 632 401 gm 645 401 lin 632 403 gm 645 403 lin 632 488 gm 645 488 lin 632 490 gm 645 490 lin 632 525 gm 645 525 lin 632 527 gm 645 527 lin 660 105 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn (1)show 660 149 gm (6740)show 660 203 gm (4529971)show 660 269 gm (---)show 660 306 gm (---)show 660 343 gm (---)show 660 380 gm (---)show 660 439 gm (672)show 660 503 gm (---)show 646 82 gm 0 gr 648 82 lin 646 80 gm 648 80 lin 646 83 gm 646 131 lin 648 83 gm 648 131 lin 646 134 gm 646 134 lin 648 132 gm 648 132 lin 646 132 gm 646 132 lin 648 134 gm 648 134 lin 646 135 gm 646 182 lin 648 135 gm 648 182 lin 646 185 gm 646 185 lin 648 183 gm 648 183 lin 646 183 gm 646 183 lin 648 185 gm 648 185 lin 646 186 gm 646 253 lin 648 186 gm 648 253 lin 646 256 gm 646 256 lin 648 254 gm 648 254 lin 646 254 gm 646 254 lin 648 256 gm 648 256 lin 646 257 gm 646 290 lin 648 257 gm 648 290 lin 646 293 gm 646 293 lin 648 291 gm 648 291 lin 646 291 gm 646 291 lin 648 293 gm 648 293 lin 646 294 gm 646 327 lin 648 294 gm 648 327 lin 646 330 gm 646 330 lin 648 328 gm 648 328 lin 646 328 gm 646 328 lin 648 330 gm 648 330 lin 646 331 gm 646 364 lin 648 331 gm 648 364 lin 646 367 gm 646 367 lin 648 365 gm 648 365 lin 646 365 gm 646 365 lin 648 367 gm 648 367 lin 646 368 gm 646 400 lin 648 368 gm 648 400 lin 646 403 gm 646 403 lin 648 401 gm 648 401 lin 646 401 gm 646 401 lin 648 403 gm 648 403 lin 646 404 gm 646 487 lin 648 404 gm 648 487 lin 646 490 gm 646 490 lin 648 488 gm 648 488 lin 646 488 gm 646 488 lin 648 490 gm 648 490 lin 646 491 gm 646 524 lin 648 491 gm 648 524 lin 646 527 gm 648 527 lin 646 525 gm 648 525 lin 649 80 gm 662 80 lin 649 82 gm 662 82 lin 649 132 gm 662 132 lin 649 134 gm 662 134 lin 649 183 gm 662 183 lin 649 185 gm 662 185 lin 649 254 gm 662 254 lin 649 256 gm 662 256 lin 649 291 gm 662 291 lin 649 293 gm 662 293 lin 649 328 gm 662 328 lin 649 330 gm 662 330 lin 649 365 gm 662 365 lin 649 367 gm 662 367 lin 649 401 gm 662 401 lin 649 403 gm 662 403 lin 649 488 gm 662 488 lin 649 490 gm 662 490 lin 649 525 gm 662 525 lin 649 527 gm 662 527 lin 675 105 gm F 1 setTxMode (3)show 675 149 gm (3019)show 675 203 gm (5251659)show 675 265 gm (2.23)show 675 302 gm (0.74)show 675 339 gm (0.93)show 675 376 gm (0.16)show 675 436 gm (1740)show 675 499 gm (2.59)show 663 82 gm 0 gr 663 82 lin 663 80 gm 663 80 lin 663 83 gm 663 131 lin 663 134 gm 663 134 lin 663 132 gm 663 132 lin 663 135 gm 663 182 lin 663 185 gm 663 185 lin 663 183 gm 663 183 lin 663 186 gm 663 253 lin 663 256 gm 663 256 lin 663 254 gm 663 254 lin 663 257 gm 663 290 lin 663 293 gm 663 293 lin 663 291 gm 663 291 lin 663 294 gm 663 327 lin 663 330 gm 663 330 lin 663 328 gm 663 328 lin 663 331 gm 663 364 lin 663 367 gm 663 367 lin 663 365 gm 663 365 lin 663 368 gm 663 400 lin 663 403 gm 663 403 lin 663 401 gm 663 401 lin 663 404 gm 663 487 lin 663 490 gm 663 490 lin 663 488 gm 663 488 lin 663 491 gm 663 524 lin 663 527 gm 663 527 lin 663 525 gm 663 525 lin 664 80 gm 677 80 lin 664 82 gm 677 82 lin 664 132 gm 677 132 lin 664 134 gm 677 134 lin 664 183 gm 677 183 lin 664 185 gm 677 185 lin 664 254 gm 677 254 lin 664 256 gm 677 256 lin 664 291 gm 677 291 lin 664 293 gm 677 293 lin 664 328 gm 677 328 lin 664 330 gm 677 330 lin 664 365 gm 677 365 lin 664 367 gm 677 367 lin 664 401 gm 677 401 lin 664 403 gm 677 403 lin 664 488 gm 677 488 lin 664 490 gm 677 490 lin 664 525 gm 677 525 lin 664 527 gm 677 527 lin 690 105 gm F 1 setTxMode (5)show 690 149 gm (2216)show 690 203 gm (6322002)show 690 265 gm (3.04)show 690 302 gm (0.61)show 690 339 gm (0.92)show 690 376 gm (0.40)show 690 436 gm (2853)show 690 499 gm (4.24)show 678 82 gm 0 gr 678 82 lin 678 80 gm 678 80 lin 678 83 gm 678 131 lin 678 134 gm 678 134 lin 678 132 gm 678 132 lin 678 135 gm 678 182 lin 678 185 gm 678 185 lin 678 183 gm 678 183 lin 678 186 gm 678 253 lin 678 256 gm 678 256 lin 678 254 gm 678 254 lin 678 257 gm 678 290 lin 678 293 gm 678 293 lin 678 291 gm 678 291 lin 678 294 gm 678 327 lin 678 330 gm 678 330 lin 678 328 gm 678 328 lin 678 331 gm 678 364 lin 678 367 gm 678 367 lin 678 365 gm 678 365 lin 678 368 gm 678 400 lin 678 403 gm 678 403 lin 678 401 gm 678 401 lin 678 404 gm 678 487 lin 678 490 gm 678 490 lin 678 488 gm 678 488 lin 678 491 gm 678 524 lin 678 527 gm 678 527 lin 678 525 gm 678 525 lin 679 80 gm 692 80 lin 679 82 gm 692 82 lin 679 132 gm 692 132 lin 679 134 gm 692 134 lin 679 183 gm 692 183 lin 679 185 gm 692 185 lin 679 254 gm 692 254 lin 679 256 gm 692 256 lin 679 291 gm 692 291 lin 679 293 gm 692 293 lin 679 328 gm 692 328 lin 679 330 gm 692 330 lin 679 365 gm 692 365 lin 679 367 gm 692 367 lin 679 401 gm 692 401 lin 679 403 gm 692 403 lin 679 488 gm 692 488 lin 679 490 gm 692 490 lin 679 525 gm 692 525 lin 679 527 gm 692 527 lin 705 105 gm F 1 setTxMode (7)show 705 149 gm (1921)show 705 203 gm (7291629)show 705 265 gm (3.51)show 705 302 gm (0.50)show 705 339 gm (0.91)show 705 376 gm (0.61)show 705 436 gm (3796)show 705 499 gm (5.65)show 693 82 gm 0 gr 693 82 lin 693 80 gm 693 80 lin 693 83 gm 693 131 lin 693 134 gm 693 134 lin 693 132 gm 693 132 lin 693 135 gm 693 182 lin 693 185 gm 693 185 lin 693 183 gm 693 183 lin 693 186 gm 693 253 lin 693 256 gm 693 256 lin 693 254 gm 693 254 lin 693 257 gm 693 290 lin 693 293 gm 693 293 lin 693 291 gm 693 291 lin 693 294 gm 693 327 lin 693 330 gm 693 330 lin 693 328 gm 693 328 lin 693 331 gm 693 364 lin 693 367 gm 693 367 lin 693 365 gm 693 365 lin 693 368 gm 693 400 lin 693 403 gm 693 403 lin 693 401 gm 693 401 lin 693 404 gm 693 487 lin 693 490 gm 693 490 lin 693 488 gm 693 488 lin 693 491 gm 693 524 lin 693 527 gm 693 527 lin 693 525 gm 693 525 lin 694 80 gm 707 80 lin 694 82 gm 707 82 lin 694 132 gm 707 132 lin 694 134 gm 707 134 lin 694 183 gm 707 183 lin 694 185 gm 707 185 lin 694 254 gm 707 254 lin 694 256 gm 707 256 lin 694 291 gm 707 291 lin 694 293 gm 707 293 lin 694 328 gm 707 328 lin 694 330 gm 707 330 lin 694 365 gm 707 365 lin 694 367 gm 707 367 lin 694 401 gm 707 401 lin 694 403 gm 707 403 lin 694 488 gm 707 488 lin 694 490 gm 707 490 lin 694 525 gm 707 525 lin 694 527 gm 707 527 lin 720 105 gm F 1 setTxMode (9)show 720 149 gm (1721)show 720 203 gm (8300115)show 720 265 gm (3.92)show 720 302 gm (0.44)show 720 339 gm (0.91)show 720 376 gm (0.83)show 720 436 gm (4823)show 720 499 gm (7.18)show 708 82 gm 0 gr 708 82 lin 708 80 gm 708 80 lin 708 83 gm 708 131 lin 708 134 gm 708 134 lin 708 132 gm 708 132 lin 708 135 gm 708 182 lin 708 185 gm 708 185 lin 708 183 gm 708 183 lin 708 186 gm 708 253 lin 708 256 gm 708 256 lin 708 254 gm 708 254 lin 708 257 gm 708 290 lin 708 293 gm 708 293 lin 708 291 gm 708 291 lin 708 294 gm 708 327 lin 708 330 gm 708 330 lin 708 328 gm 708 328 lin 708 331 gm 708 364 lin 708 367 gm 708 367 lin 708 365 gm 708 365 lin 708 368 gm 708 400 lin 708 403 gm 708 403 lin 708 401 gm 708 401 lin 708 404 gm 708 487 lin 708 490 gm 708 490 lin 708 488 gm 708 488 lin 708 491 gm 708 524 lin 708 527 gm 708 527 lin 708 525 gm 708 525 lin 709 80 gm 722 80 lin 709 82 gm 722 82 lin 709 132 gm 722 132 lin 709 134 gm 722 134 lin 709 183 gm 722 183 lin 709 185 gm 722 185 lin 709 254 gm 722 254 lin 709 256 gm 722 256 lin 709 291 gm 722 291 lin 709 293 gm 722 293 lin 709 328 gm 722 328 lin 709 330 gm 722 330 lin 709 365 gm 722 365 lin 709 367 gm 722 367 lin 709 401 gm 722 401 lin 709 403 gm 722 403 lin 709 488 gm 722 488 lin 709 490 gm 722 490 lin 709 525 gm 722 525 lin 709 527 gm 722 527 lin 735 103 gm F 1 setTxMode (11)show 735 149 gm (1600)show 735 203 gm (9439299)show 735 265 gm (4.21)show 735 302 gm (0.38)show 735 339 gm (0.90)show 735 376 gm (1.08)show 735 436 gm (5900)show 735 499 gm (8.78)show 723 82 gm 0 gr 723 82 lin 723 80 gm 723 80 lin 723 83 gm 723 131 lin 723 134 gm 723 134 lin 723 132 gm 723 132 lin 723 135 gm 723 182 lin 723 185 gm 723 185 lin 723 183 gm 723 183 lin 723 186 gm 723 253 lin 723 256 gm 723 256 lin 723 254 gm 723 254 lin 723 257 gm 723 290 lin 723 293 gm 723 293 lin 723 291 gm 723 291 lin 723 294 gm 723 327 lin 723 330 gm 723 330 lin 723 328 gm 723 328 lin 723 331 gm 723 364 lin 723 367 gm 723 367 lin 723 365 gm 723 365 lin 723 368 gm 723 400 lin 723 403 gm 723 403 lin 723 401 gm 723 401 lin 723 404 gm 723 487 lin 723 490 gm 723 490 lin 723 488 gm 723 488 lin 723 491 gm 723 524 lin 723 527 gm 723 527 lin 723 525 gm 723 525 lin 724 80 gm 737 80 lin 724 82 gm 737 82 lin 740 80 gm 740 82 lin 738 80 gm 740 80 lin 738 82 gm 738 82 lin 738 82 lin 738 83 gm 738 131 lin 740 83 gm 740 131 lin 724 132 gm 737 132 lin 724 134 gm 737 134 lin 738 132 gm 738 134 lin 740 132 gm 740 134 lin 738 135 gm 738 182 lin 740 135 gm 740 182 lin 724 183 gm 737 183 lin 724 185 gm 737 185 lin 738 183 gm 738 185 lin 740 183 gm 740 185 lin 738 186 gm 738 253 lin 740 186 gm 740 253 lin 724 254 gm 737 254 lin 724 256 gm 737 256 lin 738 254 gm 738 256 lin 740 254 gm 740 256 lin 738 257 gm 738 290 lin 740 257 gm 740 290 lin 724 291 gm 737 291 lin 724 293 gm 737 293 lin 738 291 gm 738 293 lin 740 291 gm 740 293 lin 738 294 gm 738 327 lin 740 294 gm 740 327 lin 724 328 gm 737 328 lin 724 330 gm 737 330 lin 738 328 gm 738 330 lin 740 328 gm 740 330 lin 738 331 gm 738 364 lin 740 331 gm 740 364 lin 724 365 gm 737 365 lin 724 367 gm 737 367 lin 738 365 gm 738 367 lin 740 365 gm 740 367 lin 738 368 gm 738 400 lin 740 368 gm 740 400 lin 724 401 gm 737 401 lin 724 403 gm 737 403 lin 738 401 gm 738 403 lin 740 401 gm 740 403 lin 738 404 gm 738 487 lin 740 404 gm 740 487 lin 724 488 gm 737 488 lin 724 490 gm 737 490 lin 738 488 gm 738 490 lin 740 488 gm 740 490 lin 738 491 gm 738 524 lin 740 491 gm 740 524 lin 724 525 gm 737 525 lin 724 527 gm 737 527 lin 740 525 gm 740 527 lin 738 527 gm 740 527 lin 738 525 gm 738 525 lin 738 525 lin 752 79 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (Fig.15)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( )show 2 fs bu fc 2 F /|______Times-Italic fnt bn (Dynamic splitting of top level)show F T cp %%Page: ? 15 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 336 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Helvetica fnt bn (A Comparison of Parallel Search Algorithms)show 773 79 gm (UBLCS-94-14)show 773 514 gm (13)show 122 79 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn 1.24938 0. 32 0.12493 0.(Compare this table with Fig.9. The average production factor is improved \(0.71)awidthshow 122 452 gm bu fc 2 F /|______Symbol fnt bn 0.69747 0.(\256)ashow bu fc 2 F /|______Times-Roman fnt bn 1.14624 0. 32 0.11462 0.(0.90 with 11)awidthshow 134 79 gm 1.77536 0. 32 0.17753 0.(processors\): this means that load balancing was better. More interestingly, such parameter is)awidthshow 145 79 gm 0.11734 0. 32 0.01173 0.(constant: the difference between 3 and 11 processors amounts only to 3%, so that there is little room)awidthshow 156 79 gm 0.57464 0. 32 0.05746 0.(to improve such values applying dynamic splitting also at lower levels of the game tree. Although)awidthshow 167 79 gm 0.54336 0. 32 0.05433 0.(search overhead is very high \(108% with 11 processors\), this waste does not overcome the gain in)awidthshow 178 79 gm (synchronisation overhead.)show 189 79 gm 0.50170 0. 32 0.05017 0.(We have also tested a dynamic version of PVSplit, enriched with iterative deepening and top level)awidthshow 200 79 gm (sorting; no global score is implemented \(Fig.16\).)show 229 96 gm 1 fs 10 fz bu fc 2 F /|______Times-Bold fnt bn (Procs)show 229 145 gm (T\312\(sec\))show 229 200 gm (N\312\(nodes\))show 229 271 gm (S)show 229 308 gm (E)show 229 338 gm (Fpm)show 229 378 gm (SO)show 229 416 gm (SS\312\(nodes/sec\))show 229 504 gm (Ss)show 215 80 gm 0 gr 215 82 lin 215 80 gm 217 80 lin 217 82 gm 217 82 lin 217 82 lin 215 83 gm 215 131 lin 217 83 gm 217 131 lin 215 132 gm 215 134 lin 217 132 gm 217 134 lin 215 135 gm 215 182 lin 217 135 gm 217 182 lin 215 183 gm 215 185 lin 217 183 gm 217 185 lin 215 186 gm 215 253 lin 217 186 gm 217 253 lin 215 254 gm 215 256 lin 217 254 gm 217 256 lin 215 257 gm 215 290 lin 217 257 gm 217 290 lin 215 291 gm 215 293 lin 217 291 gm 217 293 lin 215 294 gm 215 327 lin 217 294 gm 217 327 lin 215 328 gm 215 330 lin 217 328 gm 217 330 lin 215 331 gm 215 364 lin 217 331 gm 217 364 lin 215 365 gm 215 367 lin 217 365 gm 217 367 lin 215 368 gm 215 400 lin 217 368 gm 217 400 lin 215 401 gm 215 403 lin 217 401 gm 217 403 lin 215 404 gm 215 487 lin 217 404 gm 217 487 lin 215 488 gm 215 490 lin 217 488 gm 217 490 lin 215 491 gm 215 524 lin 217 491 gm 217 524 lin 215 525 gm 215 527 lin 217 527 lin 217 525 gm 217 525 lin 217 525 lin 218 80 gm 231 80 lin 218 82 gm 231 82 lin 218 132 gm 231 132 lin 218 134 gm 231 134 lin 218 183 gm 231 183 lin 218 185 gm 231 185 lin 218 254 gm 231 254 lin 218 256 gm 231 256 lin 218 291 gm 231 291 lin 218 293 gm 231 293 lin 218 328 gm 231 328 lin 218 330 gm 231 330 lin 218 365 gm 231 365 lin 218 367 gm 231 367 lin 218 401 gm 231 401 lin 218 403 gm 231 403 lin 218 488 gm 231 488 lin 218 490 gm 231 490 lin 218 525 gm 231 525 lin 218 527 gm 231 527 lin 246 105 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn (1)show 246 149 gm (6740)show 246 203 gm (4529971)show 246 269 gm (---)show 246 306 gm (---)show 246 343 gm (---)show 246 380 gm (---)show 246 439 gm (672)show 246 503 gm (---)show 232 82 gm 0 gr 234 82 lin 232 80 gm 234 80 lin 232 83 gm 232 131 lin 234 83 gm 234 131 lin 232 134 gm 232 134 lin 234 132 gm 234 132 lin 232 132 gm 232 132 lin 234 134 gm 234 134 lin 232 135 gm 232 182 lin 234 135 gm 234 182 lin 232 185 gm 232 185 lin 234 183 gm 234 183 lin 232 183 gm 232 183 lin 234 185 gm 234 185 lin 232 186 gm 232 253 lin 234 186 gm 234 253 lin 232 256 gm 232 256 lin 234 254 gm 234 254 lin 232 254 gm 232 254 lin 234 256 gm 234 256 lin 232 257 gm 232 290 lin 234 257 gm 234 290 lin 232 293 gm 232 293 lin 234 291 gm 234 291 lin 232 291 gm 232 291 lin 234 293 gm 234 293 lin 232 294 gm 232 327 lin 234 294 gm 234 327 lin 232 330 gm 232 330 lin 234 328 gm 234 328 lin 232 328 gm 232 328 lin 234 330 gm 234 330 lin 232 331 gm 232 364 lin 234 331 gm 234 364 lin 232 367 gm 232 367 lin 234 365 gm 234 365 lin 232 365 gm 232 365 lin 234 367 gm 234 367 lin 232 368 gm 232 400 lin 234 368 gm 234 400 lin 232 403 gm 232 403 lin 234 401 gm 234 401 lin 232 401 gm 232 401 lin 234 403 gm 234 403 lin 232 404 gm 232 487 lin 234 404 gm 234 487 lin 232 490 gm 232 490 lin 234 488 gm 234 488 lin 232 488 gm 232 488 lin 234 490 gm 234 490 lin 232 491 gm 232 524 lin 234 491 gm 234 524 lin 232 527 gm 234 527 lin 232 525 gm 234 525 lin 235 80 gm 248 80 lin 235 82 gm 248 82 lin 235 132 gm 248 132 lin 235 134 gm 248 134 lin 235 183 gm 248 183 lin 235 185 gm 248 185 lin 235 254 gm 248 254 lin 235 256 gm 248 256 lin 235 291 gm 248 291 lin 235 293 gm 248 293 lin 235 328 gm 248 328 lin 235 330 gm 248 330 lin 235 365 gm 248 365 lin 235 367 gm 248 367 lin 235 401 gm 248 401 lin 235 403 gm 248 403 lin 235 488 gm 248 488 lin 235 490 gm 248 490 lin 235 525 gm 248 525 lin 235 527 gm 248 527 lin 261 105 gm F 1 setTxMode (3)show 261 149 gm (2532)show 261 203 gm (4899016)show 261 265 gm (2.66)show 261 302 gm (0.89)show 261 339 gm (0.90)show 261 376 gm (0.08)show 261 436 gm (1935)show 261 499 gm (2.88)show 249 82 gm 0 gr 249 82 lin 249 80 gm 249 80 lin 249 83 gm 249 131 lin 249 134 gm 249 134 lin 249 132 gm 249 132 lin 249 135 gm 249 182 lin 249 185 gm 249 185 lin 249 183 gm 249 183 lin 249 186 gm 249 253 lin 249 256 gm 249 256 lin 249 254 gm 249 254 lin 249 257 gm 249 290 lin 249 293 gm 249 293 lin 249 291 gm 249 291 lin 249 294 gm 249 327 lin 249 330 gm 249 330 lin 249 328 gm 249 328 lin 249 331 gm 249 364 lin 249 367 gm 249 367 lin 249 365 gm 249 365 lin 249 368 gm 249 400 lin 249 403 gm 249 403 lin 249 401 gm 249 401 lin 249 404 gm 249 487 lin 249 490 gm 249 490 lin 249 488 gm 249 488 lin 249 491 gm 249 524 lin 249 527 gm 249 527 lin 249 525 gm 249 525 lin 250 80 gm 263 80 lin 250 82 gm 263 82 lin 250 132 gm 263 132 lin 250 134 gm 263 134 lin 250 183 gm 263 183 lin 250 185 gm 263 185 lin 250 254 gm 263 254 lin 250 256 gm 263 256 lin 250 291 gm 263 291 lin 250 293 gm 263 293 lin 250 328 gm 263 328 lin 250 330 gm 263 330 lin 250 365 gm 263 365 lin 250 367 gm 263 367 lin 250 401 gm 263 401 lin 250 403 gm 263 403 lin 250 488 gm 263 488 lin 250 490 gm 263 490 lin 250 525 gm 263 525 lin 250 527 gm 263 527 lin 276 105 gm F 1 setTxMode (5)show 276 149 gm (1805)show 276 203 gm (5453978)show 276 265 gm (3.73)show 276 302 gm (0.75)show 276 339 gm (0.88)show 276 376 gm (0.20)show 276 436 gm (3022)show 276 499 gm (4.50)show 264 82 gm 0 gr 264 82 lin 264 80 gm 264 80 lin 264 83 gm 264 131 lin 264 134 gm 264 134 lin 264 132 gm 264 132 lin 264 135 gm 264 182 lin 264 185 gm 264 185 lin 264 183 gm 264 183 lin 264 186 gm 264 253 lin 264 256 gm 264 256 lin 264 254 gm 264 254 lin 264 257 gm 264 290 lin 264 293 gm 264 293 lin 264 291 gm 264 291 lin 264 294 gm 264 327 lin 264 330 gm 264 330 lin 264 328 gm 264 328 lin 264 331 gm 264 364 lin 264 367 gm 264 367 lin 264 365 gm 264 365 lin 264 368 gm 264 400 lin 264 403 gm 264 403 lin 264 401 gm 264 401 lin 264 404 gm 264 487 lin 264 490 gm 264 490 lin 264 488 gm 264 488 lin 264 491 gm 264 524 lin 264 527 gm 264 527 lin 264 525 gm 264 525 lin 265 80 gm 278 80 lin 265 82 gm 278 82 lin 265 132 gm 278 132 lin 265 134 gm 278 134 lin 265 183 gm 278 183 lin 265 185 gm 278 185 lin 265 254 gm 278 254 lin 265 256 gm 278 256 lin 265 291 gm 278 291 lin 265 293 gm 278 293 lin 265 328 gm 278 328 lin 265 330 gm 278 330 lin 265 365 gm 278 365 lin 265 367 gm 278 367 lin 265 401 gm 278 401 lin 265 403 gm 278 403 lin 265 488 gm 278 488 lin 265 490 gm 278 490 lin 265 525 gm 278 525 lin 265 527 gm 278 527 lin 291 105 gm F 1 setTxMode (7)show 291 149 gm (1486)show 291 203 gm (5886412)show 291 265 gm (4.54)show 291 302 gm (0.65)show 291 339 gm (0.87)show 291 376 gm (0.30)show 291 436 gm (3961)show 291 499 gm (5.89)show 279 82 gm 0 gr 279 82 lin 279 80 gm 279 80 lin 279 83 gm 279 131 lin 279 134 gm 279 134 lin 279 132 gm 279 132 lin 279 135 gm 279 182 lin 279 185 gm 279 185 lin 279 183 gm 279 183 lin 279 186 gm 279 253 lin 279 256 gm 279 256 lin 279 254 gm 279 254 lin 279 257 gm 279 290 lin 279 293 gm 279 293 lin 279 291 gm 279 291 lin 279 294 gm 279 327 lin 279 330 gm 279 330 lin 279 328 gm 279 328 lin 279 331 gm 279 364 lin 279 367 gm 279 367 lin 279 365 gm 279 365 lin 279 368 gm 279 400 lin 279 403 gm 279 403 lin 279 401 gm 279 401 lin 279 404 gm 279 487 lin 279 490 gm 279 490 lin 279 488 gm 279 488 lin 279 491 gm 279 524 lin 279 527 gm 279 527 lin 279 525 gm 279 525 lin 280 80 gm 293 80 lin 280 82 gm 293 82 lin 280 132 gm 293 132 lin 280 134 gm 293 134 lin 280 183 gm 293 183 lin 280 185 gm 293 185 lin 280 254 gm 293 254 lin 280 256 gm 293 256 lin 280 291 gm 293 291 lin 280 293 gm 293 293 lin 280 328 gm 293 328 lin 280 330 gm 293 330 lin 280 365 gm 293 365 lin 280 367 gm 293 367 lin 280 401 gm 293 401 lin 280 403 gm 293 403 lin 280 488 gm 293 488 lin 280 490 gm 293 490 lin 280 525 gm 293 525 lin 280 527 gm 293 527 lin 306 105 gm F 1 setTxMode (9)show 306 149 gm (1315)show 306 203 gm (6386703)show 306 265 gm (5.13)show 306 302 gm (0.57)show 306 339 gm (0.84)show 306 376 gm (0.41)show 306 436 gm (4857)show 306 499 gm (7.23)show 294 82 gm 0 gr 294 82 lin 294 80 gm 294 80 lin 294 83 gm 294 131 lin 294 134 gm 294 134 lin 294 132 gm 294 132 lin 294 135 gm 294 182 lin 294 185 gm 294 185 lin 294 183 gm 294 183 lin 294 186 gm 294 253 lin 294 256 gm 294 256 lin 294 254 gm 294 254 lin 294 257 gm 294 290 lin 294 293 gm 294 293 lin 294 291 gm 294 291 lin 294 294 gm 294 327 lin 294 330 gm 294 330 lin 294 328 gm 294 328 lin 294 331 gm 294 364 lin 294 367 gm 294 367 lin 294 365 gm 294 365 lin 294 368 gm 294 400 lin 294 403 gm 294 403 lin 294 401 gm 294 401 lin 294 404 gm 294 487 lin 294 490 gm 294 490 lin 294 488 gm 294 488 lin 294 491 gm 294 524 lin 294 527 gm 294 527 lin 294 525 gm 294 525 lin 295 80 gm 308 80 lin 295 82 gm 308 82 lin 295 132 gm 308 132 lin 295 134 gm 308 134 lin 295 183 gm 308 183 lin 295 185 gm 308 185 lin 295 254 gm 308 254 lin 295 256 gm 308 256 lin 295 291 gm 308 291 lin 295 293 gm 308 293 lin 295 328 gm 308 328 lin 295 330 gm 308 330 lin 295 365 gm 308 365 lin 295 367 gm 308 367 lin 295 401 gm 308 401 lin 295 403 gm 308 403 lin 295 488 gm 308 488 lin 295 490 gm 308 490 lin 295 525 gm 308 525 lin 295 527 gm 308 527 lin 321 103 gm F 1 setTxMode (11)show 321 149 gm (1208)show 321 203 gm (6789922)show 321 265 gm (5.58)show 321 302 gm (0.51)show 321 339 gm (0.80)show 321 376 gm (0.50)show 321 436 gm (5621)show 321 499 gm (8.36)show 309 82 gm 0 gr 309 82 lin 309 80 gm 309 80 lin 309 83 gm 309 131 lin 309 134 gm 309 134 lin 309 132 gm 309 132 lin 309 135 gm 309 182 lin 309 185 gm 309 185 lin 309 183 gm 309 183 lin 309 186 gm 309 253 lin 309 256 gm 309 256 lin 309 254 gm 309 254 lin 309 257 gm 309 290 lin 309 293 gm 309 293 lin 309 291 gm 309 291 lin 309 294 gm 309 327 lin 309 330 gm 309 330 lin 309 328 gm 309 328 lin 309 331 gm 309 364 lin 309 367 gm 309 367 lin 309 365 gm 309 365 lin 309 368 gm 309 400 lin 309 403 gm 309 403 lin 309 401 gm 309 401 lin 309 404 gm 309 487 lin 309 490 gm 309 490 lin 309 488 gm 309 488 lin 309 491 gm 309 524 lin 309 527 gm 309 527 lin 309 525 gm 309 525 lin 310 80 gm 323 80 lin 310 82 gm 323 82 lin 326 80 gm 326 82 lin 324 80 gm 326 80 lin 324 82 gm 324 82 lin 324 82 lin 324 83 gm 324 131 lin 326 83 gm 326 131 lin 310 132 gm 323 132 lin 310 134 gm 323 134 lin 324 132 gm 324 134 lin 326 132 gm 326 134 lin 324 135 gm 324 182 lin 326 135 gm 326 182 lin 310 183 gm 323 183 lin 310 185 gm 323 185 lin 324 183 gm 324 185 lin 326 183 gm 326 185 lin 324 186 gm 324 253 lin 326 186 gm 326 253 lin 310 254 gm 323 254 lin 310 256 gm 323 256 lin 324 254 gm 324 256 lin 326 254 gm 326 256 lin 324 257 gm 324 290 lin 326 257 gm 326 290 lin 310 291 gm 323 291 lin 310 293 gm 323 293 lin 324 291 gm 324 293 lin 326 291 gm 326 293 lin 324 294 gm 324 327 lin 326 294 gm 326 327 lin 310 328 gm 323 328 lin 310 330 gm 323 330 lin 324 328 gm 324 330 lin 326 328 gm 326 330 lin 324 331 gm 324 364 lin 326 331 gm 326 364 lin 310 365 gm 323 365 lin 310 367 gm 323 367 lin 324 365 gm 324 367 lin 326 365 gm 326 367 lin 324 368 gm 324 400 lin 326 368 gm 326 400 lin 310 401 gm 323 401 lin 310 403 gm 323 403 lin 324 401 gm 324 403 lin 326 401 gm 326 403 lin 324 404 gm 324 487 lin 326 404 gm 326 487 lin 310 488 gm 323 488 lin 310 490 gm 323 490 lin 324 488 gm 324 490 lin 326 488 gm 326 490 lin 324 491 gm 324 524 lin 326 491 gm 326 524 lin 310 525 gm 323 525 lin 310 527 gm 323 527 lin 326 525 gm 326 527 lin 324 527 gm 326 527 lin 324 525 gm 324 525 lin 324 525 lin 338 79 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (Fig.16)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( )show 2 fs bu fc 2 F /|______Times-Italic fnt bn (Dynamic PVSplit)show 354 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.38436 0. 32 0.03843 0.(Search overhead is low, and efficiency is good: the speedup S with 11 processors was improved of)awidthshow 365 79 gm (24% with respect to data shown in\312Fig.11.)show 395 79 gm 1 fs 12 fz bu fc 2 F /|______Times-Bold fnt bn (5.2 A discussion of dynamic splitting)show 408 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.89706 0. 32 0.08970 0.(The algorithm described in Sect. 5.1 is not really representative of dynamic splitting methods. A)awidthshow 419 79 gm (more general definition of such a concept should answer to the following questions:)show 431 88 gm (\245\312when a supervisor process P visiting a node N should create a new parallel task?)show 444 88 gm (\245\312who executes the task?)show 457 88 gm (\245\312which data can be use to make a splitting decision?)show 469 79 gm 0.21591 0. 32 0.02159 0.(Consider the game tree in Fig.17; process P is responsible of its evaluation because it was given the)awidthshow 484 79 gm 0.60699 0. 32 0.06069 0.(root. According to the depth)awidthshow 484 207 gm 0.67794 0. 32 0.06779 0.(-first rule used in )awidthshow 484 289 gm bu fc 2 F /|______Symbol fnt bn 0.20346 0.(ab)ashow bu fc 2 F /|______Times-Roman fnt bn 0.57464 0. 32 0.05746 0.(, we have the following sequence for successors:)awidthshow 496 79 gm (N)show 9 fz bu fc 2 F /|______Times-Roman fnt bn (1)show 11 fz bu fc 2 F /|______Times-Roman fnt bn (, N)show 496 103 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (2)show 11 fz bu fc 2 F /|______Times-Roman fnt bn (, N)show 496 120 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn (3)show 11 fz bu fc 2 F /|______Times-Roman fnt bn (.)show (nc 520 237 675 366 6 rc)kp 0 gr 601.5 241.5 628.5 268.5 0 ov 601.5 285.5 628.5 312.5 0 ov 601.5 329.5 628.5 356.5 0 ov 522.5 285.5 548.5 312.5 0 ov 616 250 gm (nc 608 249 619 261 6 rc)kp F 1 setTxMode 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (1)show 617 295 gm (nc 609 294 620 306 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (2)show 616 339 gm (nc 608 338 619 350 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (N)show 7 fz bu fc 2 F /|______Helvetica fnt bn (3)show 538 316 gm (nc 530 315 541 323 6 rc)kp 9 fz bu fc 2 F /|______Helvetica fnt bn (P)show 601 299 gm (nc 520 237 675 366 6 rc)kp 0 gr 548 299 lin 601 343 lin 0 0 2 9 6 2 dh 548 299 gm 601 255 lin rh psb pse 0 0 2 9 6 2 dh 599 239 gm 628 271 lin rh psb pse 0 0 2 9 6 2 dh 628 240 gm 595 268 lin rh psb pse 617 359 gm (nc 608 358 620 365 6 rc)kp F 1 setTxMode 10 fz bu fc 2 F /|______Helvetica fnt bn (?)show 616 315 gm (nc 607 314 619 321 6 rc)kp (?)show 628 299 gm (nc 520 237 675 366 6 rc)kp 0 gr 673 282 lin 628 299 gm 673 311 lin 673 282 gm 673 311 lin 0 0 2 9 6 2 dh 628 255 gm 673 239 lin rh psb pse 0 0 2 9 6 2 dh 628 255 gm 673 268 lin rh psb pse 0 0 2 9 6 2 dh 673 239 gm 673 268 lin rh psb pse 628 343 gm 673 326 lin 628 343 gm 673 355 lin 673 326 gm 673 355 lin 537 290 gm (nc 529 289 540 310 6 rc)kp F 1 setTxMode 9 fz bu fc 2 F /|______Helvetica fnt bn (Root)show 509 77 gm (nc 30 28 811 566 6 rc)kp 0 gr 509 525 lin 703 131 gm F 1 setTxMode 11 fz bu fc 2 F /|______Times-Roman fnt bn (Fig.17)show 1 fs bu fc 2 F /|______Times-Bold fnt bn ( Problems with dynamic splitting: who has to evaluate N2 and N3?)show 721 77 gm 0 gr 721 525 lin 740 79 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.05569 0. 32 0.00556 0.(Suppose the subtree with root N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn (1)show 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.04531 0. 32 0.00453 0.( has been evaluated; if no cuts were produced P has to start the visit)awidthshow 751 79 gm 0.49194 0. 32 0.04919 0.(of N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.15614 0.(2)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.47515 0. 32 0.04751 0.(, i.e. it generates the task of visiting N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.15614 0.(2)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.45867 0. 32 0.04586 0.(. It can happen that P itself is assigned to this task, so)awidthshow F T cp %%Page: ? 16 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 336 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Helvetica fnt bn (A Comparison of Parallel Search Algorithms)show 773 79 gm (UBLCS-94-14)show 773 514 gm (14)show 118 79 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.66665 0. 32 0.06666 0.(that only when such a visit is completed N)awidthshow 118 274 gm 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.20846 0.(3)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.66177 0. 32 0.06617 0.( will be evaluated, unless a cut is produced. If P were)awidthshow 129 79 gm 0.21484 0. 32 0.02148 0.(assigned all successors of the root node shown in Fig.17, then actually no splitting would have been)awidthshow 140 79 gm 0.04959 0. 32 0.00495 0.(done in the root. Instead, suppose that N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn (2)show 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.04257 0. 32 0.00425 0.( is given to a process Q different from P; then, P should not)awidthshow 151 79 gm 0.30273 0. 32 0.03027 0.(block itself waiting for Q, but should continue the visit and allocate a task for the evaluation of N)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.08947 0.(3)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn (.)show 162 79 gm 0.87707 0. 32 0.08770 0.(In this way we have a splitting only if this is really necessary; moreover, we improve control on)awidthshow 173 79 gm (search overhead and load balancing.)show 184 79 gm 1.54342 0. 32 0.15434 0.(An important decision when using of this kind of algorithm is the knowledge necessary for a)awidthshow 195 79 gm 0.94299 0. 32 0.09429 0.(splitting. There are two kinds of knowledge that are necessary for a process P to take a splitting)awidthshow 206 79 gm (decision on a node N:)show 218 88 gm 0.76568 0. 32 0.07656 0.(- local knowledge, )awidthshow 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.15858 0.(i.e)ashow 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.63476 0. 32 0.06347 0.(. data owned by the process P itself that is going to decide a splitting. For)awidthshow 229 101 gm 0.12954 0. 32 0.01295 0.(instance, knowledge on the level of N in the game tree, or on the size of the subtree whose root)awidthshow 240 101 gm (is N, is local.)show 253 88 gm 0.03265 0. 32 0.00326 0.(- global knowledge, )awidthshow 253 178 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn (i.e)show 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.02944 0. 32 0.00294 0.(. data that have to be asked to the operating environment. For instance, how)awidthshow 264 101 gm 1.16287 0. 32 0.11628 0.(many processors are idle or how many tasks are still in the agenda are examples of global)awidthshow 275 101 gm (knowledge.)show 287 79 gm 0.30563 0. 32 0.03056 0.(Suppose that in order to decide if N is a splitting node we only use knowledge local to P, assigning)awidthshow 298 79 gm 0.62866 0. 32 0.06286 0.(N and its subtree to P itself: the decision will be very rapid. However, load balancing will rapidly)awidthshow 309 79 gm 0.19454 0. 32 0.01945 0.(deteriorate. Thus, we need to combine both form of knowledge; we achieve this taking a decision in)awidthshow 320 79 gm (two steps:)show 332 88 gm (i\)\312let P be the supervisor of N; we make a local test to see if P itself can take charge of N;)show 345 88 gm 0.44586 0. 32 0.04458 0.(ii\)\312if not, we use global knowledge to choose a different supervisor. This implies communicating)awidthshow 356 101 gm (with other processes.)show 368 79 gm 1.46865 0. 32 0.14686 0.(We put all global data in tuples: both the task to be assigned to a worker, corresponding to a)awidthshow 379 79 gm 0.64743 0. 32 0.06474 0.(splitting, and data to make splitting decisions. A node N becomes a splitting node when search of)awidthshow 390 79 gm 0.07965 0. 32 0.00796 0.(one of its children is given to another process. A splitting decision needs data that can be either local)awidthshow 401 79 gm 0.11535 0. 32 0.01153 0.(or non-local. In general non-local data are more expensive to acquire, thus we classify splitting rules)awidthshow 412 79 gm 0.48583 0. 32 0.04858 0.(built in the Boolean function as local or global. Local rules say when it is not convenient to start a)awidthshow 423 79 gm (parallel task; if local rules require splitting, then global data are acquired.)show 434 79 gm (This is a very partial list of criteria based on local data:)show 446 88 gm 1.15356 0. 32 0.11535 0.(\245\312subtree size: small subtrees are not distributed. Subtree size should be measured in terms of)awidthshow 457 101 gm 0.61340 0. 32 0.06134 0.(nodes, but this figure is not known before the visit; however, it is possible to estimate such a)awidthshow 472 101 gm 0.11322 0. 32 0.01132 0.(quantity knowing the tree depth and the wideness of the initial )awidthshow bu fc 2 F /|______Symbol fnt bn 0.04614 0.(ab)ashow bu fc 2 F /|______Times-Roman fnt bn 0.14205 0. 32 0.01420 0.( window [Bau78]. A measure)awidthshow 484 101 gm (simpler to obtain is given by the tree depth [Eli90].)show 497 88 gm 0.10589 0. 32 0.01058 0.(\245\312"young-brothers-wait" [FMMV89]: aims at reducing search overhead if the game tree is ordered.)awidthshow 508 101 gm 0.99380 0. 32 0.09938 0.(The first successor of a node has to be completely evaluated before proceeding in the visit.)awidthshow 519 101 gm 2.21588 0. 32 0.22158 0.(Thus a node N has to be evaluated by its supervisor if it is the first to be visited. A)awidthshow 530 101 gm 2.09609 0. 32 0.20960 0.(generalisation of this method consists of avoiding the distribution of the first K \(K>1\))awidthshow 541 101 gm 0.37506 0. 32 0.03750 0.(successors. For ordered game trees the best moves are with high probability "on the left", thus)awidthshow 556 101 gm (if we give priority to this side we get better )show 556 293 gm bu fc 2 F /|______Symbol fnt bn (ab)show bu fc 2 F /|______Times-Roman fnt bn ( windows for continuing the search in parallel.)show 570 88 gm 1.08642 0. 32 0.10864 0.(\245\312limiting the max. number of children visited in parallel: the idea is to get a good amount of)awidthshow 581 101 gm 1.09680 0. 32 0.10968 0.(information from incomplete searches. The supervisor only need to know how many nodes)awidthshow 592 101 gm (were distributed but not yet entirely searched.)show 604 79 gm (The following criteria are based on global knowledge:)show 616 88 gm 0.44174 0. 32 0.04417 0.(\245\312limiting the number of tasks in agenda, aiming at reducing synchronisation overhead. In fact, if)awidthshow 627 101 gm 1.18713 0. 32 0.11871 0.(tasks were too many with respect to the available processors, the task originators could be)awidthshow 638 101 gm 1.72622 0. 32 0.17262 0.(strongly slowed. A typical value that can be chosen as maximum is the total number of)awidthshow 649 101 gm 0.63552 0. 32 0.06355 0.(processors. We put a counter in a single tuple; the counter is incremented by supervisors and)awidthshow 660 101 gm (decremented by workers.)show 673 88 gm 0.15594 0. 32 0.01559 0.(\245\312splitting only in case of idle processor: we avoid that a task remains too much time in agenda, so)awidthshow 684 101 gm 1.12258 0. 32 0.11225 0.(that we reduce synchronisation overhead. We need to count how many processors are idle,)awidthshow 695 101 gm (again with a counter tuple.)show 707 79 gm (Now we are ready to describe a dynamic algorithm parametric wrt the splitting rules.)show 737 79 gm 1 fs 12 fz bu fc 2 F /|______Times-Bold fnt bn (5.3 A general algorithm for dynamic splitting)show F T cp %%Page: ? 17 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 336 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Helvetica fnt bn (A Comparison of Parallel Search Algorithms)show 773 79 gm (UBLCS-94-14)show 773 514 gm (15)show 118 79 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn 1.21017 0. 32 0.12101 0.(We have designed a software architecture that is easy to adapt to different splitting algorithms.)awidthshow 129 79 gm 0.08255 0. 32 0.00825 0.(Given a splitting criterion, we specialise the core algorithm aiming at maximising the efficiency. We)awidthshow 140 79 gm 0.30303 0. 32 0.03030 0.(note that we could treat most static splitting algorithms as special cases of trivial dynamic splitting,)awidthshow 151 79 gm 1.00021 0. 32 0.10002 0.(however we would lose most of the optimisations that were possible because the splitting nodes)awidthshow 162 79 gm (were well known or in a small number.)show 173 79 gm 1.19873 0. 32 0.11987 0.(The core algorithm for dynamic splitting allows that any node can be a splitting node. Data on)awidthshow 184 79 gm 1.79733 0. 32 0.17973 0.(arbitrary nodes is much more expensive to transmit and to receive: communication overhead)awidthshow 195 79 gm (increases, especially on a network of workstations.)show 206 79 gm 0.08758 0. 32 0.00875 0.(Moreover, each task has to be identified independently form the worker that executes it; thus to each)awidthshow 217 79 gm 1.59393 0. 32 0.15939 0.(node N we associate a signature that will be inherited by all N successors; such an idea was)awidthshow 228 79 gm 1.32034 0. 32 0.13203 0.(introduced in [Eli90]. When a cut occurs, all parallel search having the same signature will be)awidthshow 239 79 gm (terminated, because they are now useless.)show 250 79 gm 0.01724 0. 32 0.00172 0.(Each new splitting node is associated to a new signature; since in the core algorithm a parallel search)awidthshow 261 79 gm 0.26687 0. 32 0.02668 0.(can be started at any level in the tree, nodes of the same subtree obtain different signatures. When a)awidthshow 272 79 gm 0.44692 0. 32 0.04469 0.(cut is generated for the top-level of a subtree all parallel searches of its branches should terminate,)awidthshow 283 79 gm 0.81695 0. 32 0.08169 0.(even if the signatures are different. The signature is a distributed data structure whose root is the)awidthshow 294 79 gm 0.65292 0. 32 0.06529 0.(signature of the game tree root. Suppose that a node N has a signature S inherited from its father;)awidthshow 305 79 gm (suppose that N is chosen as splitting node: it get s a new signature T.)show (nc 330 96 543 506 6 rc)kp 64 gr 412 146 435 169 1 ov 0 gr 412.5 146.5 434.5 168.5 0 ov 64 gr 468 113 490 135 1 ov 0 gr 468.5 113.5 489.5 134.5 0 ov 64 gr 519 98 542 120 1 ov 0 gr 519.5 98.5 541.5 119.5 0 ov 64 gr 519 126 542 148 1 ov 0 gr 519.5 126.5 541.5 147.5 0 ov 489 124 gm 519 136 lin 489 124 gm 519 108 lin 64 gr 468 175 490 198 1 ov 0 gr 468.5 175.5 489.5 197.5 0 ov 64 gr 519 160 542 182 1 ov 0 gr 519.5 160.5 541.5 181.5 0 ov 64 gr 519 188 542 210 1 ov 0 gr 519.5 188.5 541.5 209.5 0 ov 489 186 gm 519 199 lin 489 186 gm 519 170 lin 434 156 gm 468 187 lin 434 156 gm 468 123 lin 64 gr 412 278 435 300 1 ov 0 gr 412.5 278.5 434.5 299.5 0 ov 64 gr 468 245 490 267 1 ov 0 gr 468.5 245.5 489.5 266.5 0 ov 64 gr 519 229 542 252 1 ov 0 gr 519.5 229.5 541.5 251.5 0 ov 64 gr 519 258 542 280 1 ov 0 gr 519.5 258.5 541.5 279.5 0 ov 489 256 gm 519 268 lin 0 0 2 9 6 2 dh 489 256 gm 519 240 lin rh psb pse 64 gr 468 307 490 330 1 ov 0 gr 468.5 307.5 489.5 329.5 0 ov 64 gr 519 292 542 314 1 ov 0 gr 519.5 292.5 541.5 313.5 0 ov 64 gr 519 320 542 342 1 ov 0 gr 519.5 320.5 541.5 341.5 0 ov 489 318 gm 519 331 lin 489 318 gm 519 302 lin 434 288 gm 468 319 lin 434 288 gm 468 256 lin 64 gr 413 410 436 432 1 ov 0 gr 413.5 410.5 435.5 431.5 0 ov 64 gr 468 377 490 399 1 ov 0 gr 468.5 377.5 489.5 398.5 0 ov 64 gr 519 361 542 383 1 ov 0 gr 519.5 361.5 541.5 382.5 0 ov 64 gr 519 389 542 412 1 ov 0 gr 519.5 389.5 541.5 411.5 0 ov 0 0 2 9 6 2 dh 489 387 gm 519 400 lin rh psb pse 489 387 gm 519 372 lin 64 gr 469 439 491 461 1 ov 0 gr 469.5 439.5 490.5 460.5 0 ov 64 gr 520 423 543 446 1 ov 0 gr 520.5 423.5 542.5 445.5 0 ov 64 gr 519 452 542 474 1 ov 0 gr 519.5 452.5 541.5 473.5 0 ov 489 450 gm 519 462 lin 489 450 gm 519 434 lin 434 420 gm 468 450 lin 0 0 2 9 6 2 dh 434 420 gm 468 387 lin rh psb pse 64 gr 353 278 375 300 1 ov 0 gr 353.5 278.5 374.5 299.5 0 ov 0 0 2 9 6 2 dh 374 290 gm 412 290 lin rh psb pse 0 0 2 9 6 2 dh 374 290 gm 412 158 lin rh psb pse 374 289 gm 412 420 lin 64 gr 361 282 368 300 1 rc 366 283 gm (nc 361 282 368 300 6 rc)kp F 1 setTxMode 7 fz bu fc 2 F /|______Helvetica fnt bn (0)show 366 287 gm bu fc 2 F /|______Symbol fnt bn (\256)show 366 294 gm bu fc 2 F /|______Helvetica fnt bn (1)show (nc 330 96 543 506 6 rc)kp 64 gr 417 154 429 162 1 rc 426 155 gm (nc 417 154 429 162 6 rc)kp F 1 setTxMode 10 fz bu fc 2 F /|______Helvetica fnt bn (1)show (nc 330 96 543 506 6 rc)kp 64 gr 417 285 429 293 1 rc 426 286 gm (nc 417 285 429 293 6 rc)kp F 1 setTxMode (1)show (nc 330 96 543 506 6 rc)kp 64 gr 420 413 427 430 1 rc 425 414 gm (nc 420 413 427 430 6 rc)kp F 1 setTxMode 7 fz bu fc 2 F /|______Helvetica fnt bn (1)show 425 418 gm bu fc 2 F /|______Symbol fnt bn (\256)show 425 425 gm bu fc 2 F /|______Helvetica fnt bn (2)show (nc 330 96 543 506 6 rc)kp 64 gr 475 250 482 267 1 rc 480 251 gm (nc 475 250 482 267 6 rc)kp F 1 setTxMode (1)show 480 255 gm bu fc 2 F /|______Symbol fnt bn (\256)show 480 262 gm bu fc 2 F /|______Helvetica fnt bn (3)show (nc 330 96 543 506 6 rc)kp 64 gr 524 267 536 275 1 rc 533 268 gm (nc 524 267 536 275 6 rc)kp F 1 setTxMode 10 fz bu fc 2 F /|______Helvetica fnt bn (3)show (nc 330 96 543 506 6 rc)kp 64 gr 525 329 537 337 1 rc 534 330 gm (nc 525 329 537 337 6 rc)kp F 1 setTxMode (1)show (nc 330 96 543 506 6 rc)kp 64 gr 523 301 535 309 1 rc 532 302 gm (nc 523 301 535 309 6 rc)kp F 1 setTxMode (1)show (nc 330 96 543 506 6 rc)kp 64 gr 524 239 536 247 1 rc 533 240 gm (nc 524 239 536 247 6 rc)kp F 1 setTxMode (3)show (nc 330 96 543 506 6 rc)kp 64 gr 473 185 485 193 1 rc 482 186 gm (nc 473 185 485 193 6 rc)kp F 1 setTxMode (1)show (nc 330 96 543 506 6 rc)kp 64 gr 524 198 536 206 1 rc 533 199 gm (nc 524 198 536 206 6 rc)kp F 1 setTxMode (1)show (nc 330 96 543 506 6 rc)kp 64 gr 524 169 536 177 1 rc 533 170 gm (nc 524 169 536 177 6 rc)kp F 1 setTxMode (1)show (nc 330 96 543 506 6 rc)kp 64 gr 524 136 536 144 1 rc 533 137 gm (nc 524 136 536 144 6 rc)kp F 1 setTxMode (1)show (nc 330 96 543 506 6 rc)kp 64 gr 524 107 536 115 1 rc 533 108 gm (nc 524 107 536 115 6 rc)kp F 1 setTxMode (1)show (nc 330 96 543 506 6 rc)kp 64 gr 472 122 484 130 1 rc 481 123 gm (nc 472 122 484 130 6 rc)kp F 1 setTxMode (1)show (nc 330 96 543 506 6 rc)kp 64 gr 471 317 483 325 1 rc 480 318 gm (nc 471 317 483 325 6 rc)kp F 1 setTxMode (1)show (nc 330 96 543 506 6 rc)kp 64 gr 474 382 481 399 1 rc 479 383 gm (nc 474 382 481 399 6 rc)kp F 1 setTxMode 7 fz bu fc 2 F /|______Helvetica fnt bn (2)show 479 387 gm bu fc 2 F /|______Symbol fnt bn (\256)show 479 394 gm bu fc 2 F /|______Helvetica fnt bn (4)show (nc 330 96 543 506 6 rc)kp 64 gr 472 448 484 456 1 rc 481 449 gm (nc 472 448 484 456 6 rc)kp F 1 setTxMode 10 fz bu fc 2 F /|______Helvetica fnt bn (2)show (nc 330 96 543 506 6 rc)kp 64 gr 524 432 536 440 1 rc 533 433 gm (nc 524 432 536 440 6 rc)kp F 1 setTxMode (2)show (nc 330 96 543 506 6 rc)kp 64 gr 524 461 536 469 1 rc 533 462 gm (nc 524 461 536 469 6 rc)kp F 1 setTxMode (2)show (nc 330 96 543 506 6 rc)kp 64 gr 524 369 536 377 1 rc 533 370 gm (nc 524 369 536 377 6 rc)kp F 1 setTxMode (4)show (nc 330 96 543 506 6 rc)kp 64 gr 524 399 536 407 1 rc 533 400 gm (nc 524 399 536 407 6 rc)kp F 1 setTxMode (4)show (nc 330 96 543 506 6 rc)kp 64 gr 376 215 388 229 1 rc 385 216 gm (nc 376 215 388 229 6 rc)kp F 1 setTxMode (\(a\))show (nc 330 96 543 506 6 rc)kp 64 gr 437 388 449 402 1 rc 446 389 gm (nc 437 388 449 402 6 rc)kp F 1 setTxMode (\(b\))show (nc 330 96 543 506 6 rc)kp 64 gr 495 232 507 246 1 rc 504 233 gm (nc 495 232 507 246 6 rc)kp F 1 setTxMode (\(c\))show (nc 330 96 543 506 6 rc)kp 64 gr 492 364 504 378 1 rc 501 365 gm (nc 492 364 504 378 6 rc)kp F 1 setTxMode (\(d\))show 0 0 pen 355 317 gm (nc 330 96 543 506 6 rc)kp 64 gr 355 317 lin nc ct 39 0 put pr 360 308 pl 355 317 pl 358 318 pl 362 318 pl 360 308 pl 4 ep 360 308 gm bp 355 317 T qi 355 317 qc 358 318 qc 358 318 qc 362 318 qc 362 318 qc 360 308 qc 360 308 T qq qf qf ef 0 gr 15 ec (nc 330 96 543 506 6 rc)kp 1 1 pen 358 318 gm 0 gr 350 376 lin 64 gr 332 377 382 506 1 rc 0 gr 332.5 377.5 381.5 505.5 0 rc 64 gr 333 386 381 494 1 rc 342 387 gm (nc 333 386 381 494 6 rc)kp F 1 setTxMode (A decomposition node)show 354 387 gm (defines a signature)show 366 387 gm (different from that)show 378 387 gm (inherited from the father)show 318 77 gm (nc 30 28 811 566 6 rc)kp 0 gr 318 525 lin 572 235 gm F 1 setTxMode 11 fz bu fc 2 F /|______Times-Roman fnt bn (Fig.18)show 1 fs bu fc 2 F /|______Times-Bold fnt bn ( Assigning a signature)show 590 77 gm 0 gr 590 525 lin 609 79 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn 0.43762 0. 32 0.04376 0.(In Fig.18 it is shown a game tree; dotted lines represents subtrees distributed to other processors; a)awidthshow 620 79 gm 0.45349 0. 32 0.04534 0.(node label is the local signature. The depicted game tree includes four local splittings. Splitting \(a\))awidthshow 631 79 gm (distributes tasks for searching leftmost subtrees; other splittings distribute a single task only.)show 661 79 gm 1 fs 12 fz bu fc 2 F /|______Times-Bold fnt bn (5.4 Results)show 674 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.35888 0. 32 0.03588 0.(We tested the algorithm for dynamic splitting with several splitting criteria; we found that the most)awidthshow 685 79 gm (interesting were the following:)show 697 88 gm 0.18385 0.(\245\312)ashow 2 fs bu fc 2 F /|______Times-Italic fnt bn 1.16302 0. 32 0.11630 0.(Policy A)awidthshow 0 fs bu fc 2 F /|______Times-Roman fnt bn 1.10183 0. 32 0.11018 0.(: local condition: young)awidthshow 697 244 gm 0.95367 0. 32 0.09536 0.(-brothers-wait without distributing small subtrees \(depth)awidthshow currentfont SwToSym 0.95367 0. 32 0.09536 0.(\243)awidthshow setfont 0.95367 0. 32 0.09536 0.(2\);)awidthshow 708 101 gm 0.14068 0. 32 0.01406 0.(global condition: splitting is allowed only if there is an idle worker and the agenda contains \(P)awidthshow 708 519 gm (-)show 719 101 gm (1\) tasks.)show 732 88 gm (\245\312)show 2 fs bu fc 2 F /|______Times-Italic fnt bn (Policy B)show 732 131 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn (: no signature tree; splitting is allowed even if there are no idle workers.)show 744 79 gm (The corresponding tests are shown in Figg.19 and 20.)show F T cp %%Page: ? 18 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 336 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Helvetica fnt bn (A Comparison of Parallel Search Algorithms)show 773 79 gm (UBLCS-94-14)show 773 514 gm (16)show 136 96 gm 1 fs bu fc 2 F /|______Times-Bold fnt bn (Procs)show 136 145 gm (T\312\(sec\))show 136 200 gm (N\312\(nodes\))show 136 271 gm (S)show 136 308 gm (E)show 136 338 gm (Fpm)show 136 378 gm (SO)show 136 416 gm (SS\312\(nodes/sec\))show 136 502 gm (Sss)show 122 80 gm 0 gr 122 82 lin 122 80 gm 124 80 lin 124 82 gm 124 82 lin 124 82 lin 122 83 gm 122 131 lin 124 83 gm 124 131 lin 122 132 gm 122 134 lin 124 132 gm 124 134 lin 122 135 gm 122 182 lin 124 135 gm 124 182 lin 122 183 gm 122 185 lin 124 183 gm 124 185 lin 122 186 gm 122 253 lin 124 186 gm 124 253 lin 122 254 gm 122 256 lin 124 254 gm 124 256 lin 122 257 gm 122 290 lin 124 257 gm 124 290 lin 122 291 gm 122 293 lin 124 291 gm 124 293 lin 122 294 gm 122 327 lin 124 294 gm 124 327 lin 122 328 gm 122 330 lin 124 328 gm 124 330 lin 122 331 gm 122 364 lin 124 331 gm 124 364 lin 122 365 gm 122 367 lin 124 365 gm 124 367 lin 122 368 gm 122 400 lin 124 368 gm 124 400 lin 122 401 gm 122 403 lin 124 401 gm 124 403 lin 122 404 gm 122 487 lin 124 404 gm 124 487 lin 122 488 gm 122 490 lin 124 488 gm 124 490 lin 122 491 gm 122 524 lin 124 491 gm 124 524 lin 122 525 gm 122 527 lin 124 527 lin 124 525 gm 124 525 lin 124 525 lin 125 80 gm 138 80 lin 125 82 gm 138 82 lin 125 132 gm 138 132 lin 125 134 gm 138 134 lin 125 183 gm 138 183 lin 125 185 gm 138 185 lin 125 254 gm 138 254 lin 125 256 gm 138 256 lin 125 291 gm 138 291 lin 125 293 gm 138 293 lin 125 328 gm 138 328 lin 125 330 gm 138 330 lin 125 365 gm 138 365 lin 125 367 gm 138 367 lin 125 401 gm 138 401 lin 125 403 gm 138 403 lin 125 488 gm 138 488 lin 125 490 gm 138 490 lin 125 525 gm 138 525 lin 125 527 gm 138 527 lin 153 105 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn (1)show 152 149 gm (8301)show 152 203 gm (5347545)show 152 269 gm (---)show 152 306 gm (---)show 152 343 gm (---)show 152 380 gm (---)show 152 439 gm (644)show 152 503 gm (---)show 139 82 gm 0 gr 141 82 lin 139 80 gm 141 80 lin 139 83 gm 139 131 lin 141 83 gm 141 131 lin 139 134 gm 139 134 lin 141 132 gm 141 132 lin 139 132 gm 139 132 lin 141 134 gm 141 134 lin 139 135 gm 139 182 lin 141 135 gm 141 182 lin 139 185 gm 139 185 lin 141 183 gm 141 183 lin 139 183 gm 139 183 lin 141 185 gm 141 185 lin 139 186 gm 139 253 lin 141 186 gm 141 253 lin 139 256 gm 139 256 lin 141 254 gm 141 254 lin 139 254 gm 139 254 lin 141 256 gm 141 256 lin 139 257 gm 139 290 lin 141 257 gm 141 290 lin 139 293 gm 139 293 lin 141 291 gm 141 291 lin 139 291 gm 139 291 lin 141 293 gm 141 293 lin 139 294 gm 139 327 lin 141 294 gm 141 327 lin 139 330 gm 139 330 lin 141 328 gm 141 328 lin 139 328 gm 139 328 lin 141 330 gm 141 330 lin 139 331 gm 139 364 lin 141 331 gm 141 364 lin 139 367 gm 139 367 lin 141 365 gm 141 365 lin 139 365 gm 139 365 lin 141 367 gm 141 367 lin 139 368 gm 139 400 lin 141 368 gm 141 400 lin 139 403 gm 139 403 lin 141 401 gm 141 401 lin 139 401 gm 139 401 lin 141 403 gm 141 403 lin 139 404 gm 139 487 lin 141 404 gm 141 487 lin 139 490 gm 139 490 lin 141 488 gm 141 488 lin 139 488 gm 139 488 lin 141 490 gm 141 490 lin 139 491 gm 139 524 lin 141 491 gm 141 524 lin 139 527 gm 141 527 lin 139 525 gm 141 525 lin 142 80 gm 155 80 lin 142 82 gm 155 82 lin 142 132 gm 155 132 lin 142 134 gm 155 134 lin 142 183 gm 155 183 lin 142 185 gm 155 185 lin 142 254 gm 155 254 lin 142 256 gm 155 256 lin 142 291 gm 155 291 lin 142 293 gm 155 293 lin 142 328 gm 155 328 lin 142 330 gm 155 330 lin 142 365 gm 155 365 lin 142 367 gm 155 367 lin 142 401 gm 155 401 lin 142 403 gm 155 403 lin 142 488 gm 155 488 lin 142 490 gm 155 490 lin 142 525 gm 155 525 lin 142 527 gm 155 527 lin 167 105 gm F 1 setTxMode (3)show 167 149 gm (3797)show 167 203 gm (6206534)show 167 265 gm (2.19)show 167 302 gm (0.73)show 167 339 gm (0.85)show 167 376 gm (0.16)show 167 436 gm (1635)show 167 499 gm (2.54)show 156 82 gm 0 gr 156 82 lin 156 80 gm 156 80 lin 156 83 gm 156 131 lin 156 134 gm 156 134 lin 156 132 gm 156 132 lin 156 135 gm 156 182 lin 156 185 gm 156 185 lin 156 183 gm 156 183 lin 156 186 gm 156 253 lin 156 256 gm 156 256 lin 156 254 gm 156 254 lin 156 257 gm 156 290 lin 156 293 gm 156 293 lin 156 291 gm 156 291 lin 156 294 gm 156 327 lin 156 330 gm 156 330 lin 156 328 gm 156 328 lin 156 331 gm 156 364 lin 156 367 gm 156 367 lin 156 365 gm 156 365 lin 156 368 gm 156 400 lin 156 403 gm 156 403 lin 156 401 gm 156 401 lin 156 404 gm 156 487 lin 156 490 gm 156 490 lin 156 488 gm 156 488 lin 156 491 gm 156 524 lin 156 527 gm 156 527 lin 156 525 gm 156 525 lin 157 80 gm 169 80 lin 157 82 gm 169 82 lin 157 132 gm 169 132 lin 157 134 gm 169 134 lin 157 183 gm 169 183 lin 157 185 gm 169 185 lin 157 254 gm 169 254 lin 157 256 gm 169 256 lin 157 291 gm 169 291 lin 157 293 gm 169 293 lin 157 328 gm 169 328 lin 157 330 gm 169 330 lin 157 365 gm 169 365 lin 157 367 gm 169 367 lin 157 401 gm 169 401 lin 157 403 gm 169 403 lin 157 488 gm 169 488 lin 157 490 gm 169 490 lin 157 525 gm 169 525 lin 157 527 gm 169 527 lin 181 105 gm F 1 setTxMode (5)show 181 149 gm (2634)show 181 203 gm (6829036)show 181 265 gm (3.15)show 181 302 gm (0.63)show 181 339 gm (0.82)show 181 376 gm (0.28)show 181 436 gm (2593)show 181 499 gm (4.02)show 170 82 gm 0 gr 170 82 lin 170 80 gm 170 80 lin 170 83 gm 170 131 lin 170 134 gm 170 134 lin 170 132 gm 170 132 lin 170 135 gm 170 182 lin 170 185 gm 170 185 lin 170 183 gm 170 183 lin 170 186 gm 170 253 lin 170 256 gm 170 256 lin 170 254 gm 170 254 lin 170 257 gm 170 290 lin 170 293 gm 170 293 lin 170 291 gm 170 291 lin 170 294 gm 170 327 lin 170 330 gm 170 330 lin 170 328 gm 170 328 lin 170 331 gm 170 364 lin 170 367 gm 170 367 lin 170 365 gm 170 365 lin 170 368 gm 170 400 lin 170 403 gm 170 403 lin 170 401 gm 170 401 lin 170 404 gm 170 487 lin 170 490 gm 170 490 lin 170 488 gm 170 488 lin 170 491 gm 170 524 lin 170 527 gm 170 527 lin 170 525 gm 170 525 lin 171 80 gm 183 80 lin 171 82 gm 183 82 lin 171 132 gm 183 132 lin 171 134 gm 183 134 lin 171 183 gm 183 183 lin 171 185 gm 183 185 lin 171 254 gm 183 254 lin 171 256 gm 183 256 lin 171 291 gm 183 291 lin 171 293 gm 183 293 lin 171 328 gm 183 328 lin 171 330 gm 183 330 lin 171 365 gm 183 365 lin 171 367 gm 183 367 lin 171 401 gm 183 401 lin 171 403 gm 183 403 lin 171 488 gm 183 488 lin 171 490 gm 183 490 lin 171 525 gm 183 525 lin 171 527 gm 183 527 lin 196 105 gm F 1 setTxMode (7)show 196 149 gm (2133)show 196 203 gm (7407997)show 196 265 gm (3.89)show 196 302 gm (0.56)show 196 339 gm (0.77)show 196 376 gm (0.39)show 196 436 gm (3473)show 196 499 gm (5.39)show 184 82 gm 0 gr 184 82 lin 184 80 gm 184 80 lin 184 83 gm 184 131 lin 184 134 gm 184 134 lin 184 132 gm 184 132 lin 184 135 gm 184 182 lin 184 185 gm 184 185 lin 184 183 gm 184 183 lin 184 186 gm 184 253 lin 184 256 gm 184 256 lin 184 254 gm 184 254 lin 184 257 gm 184 290 lin 184 293 gm 184 293 lin 184 291 gm 184 291 lin 184 294 gm 184 327 lin 184 330 gm 184 330 lin 184 328 gm 184 328 lin 184 331 gm 184 364 lin 184 367 gm 184 367 lin 184 365 gm 184 365 lin 184 368 gm 184 400 lin 184 403 gm 184 403 lin 184 401 gm 184 401 lin 184 404 gm 184 487 lin 184 490 gm 184 490 lin 184 488 gm 184 488 lin 184 491 gm 184 524 lin 184 527 gm 184 527 lin 184 525 gm 184 525 lin 185 80 gm 198 80 lin 185 82 gm 198 82 lin 185 132 gm 198 132 lin 185 134 gm 198 134 lin 185 183 gm 198 183 lin 185 185 gm 198 185 lin 185 254 gm 198 254 lin 185 256 gm 198 256 lin 185 291 gm 198 291 lin 185 293 gm 198 293 lin 185 328 gm 198 328 lin 185 330 gm 198 330 lin 185 365 gm 198 365 lin 185 367 gm 198 367 lin 185 401 gm 198 401 lin 185 403 gm 198 403 lin 185 488 gm 198 488 lin 185 490 gm 198 490 lin 185 525 gm 198 525 lin 185 527 gm 198 527 lin 211 105 gm F 1 setTxMode (9)show 211 149 gm (1878)show 211 203 gm (7810188)show 211 265 gm (4.42)show 211 302 gm (0.49)show 211 339 gm (0.74)show 211 376 gm (0.46)show 211 436 gm (4159)show 211 499 gm (6.46)show 199 82 gm 0 gr 199 82 lin 199 80 gm 199 80 lin 199 83 gm 199 131 lin 199 134 gm 199 134 lin 199 132 gm 199 132 lin 199 135 gm 199 182 lin 199 185 gm 199 185 lin 199 183 gm 199 183 lin 199 186 gm 199 253 lin 199 256 gm 199 256 lin 199 254 gm 199 254 lin 199 257 gm 199 290 lin 199 293 gm 199 293 lin 199 291 gm 199 291 lin 199 294 gm 199 327 lin 199 330 gm 199 330 lin 199 328 gm 199 328 lin 199 331 gm 199 364 lin 199 367 gm 199 367 lin 199 365 gm 199 365 lin 199 368 gm 199 400 lin 199 403 gm 199 403 lin 199 401 gm 199 401 lin 199 404 gm 199 487 lin 199 490 gm 199 490 lin 199 488 gm 199 488 lin 199 491 gm 199 524 lin 199 527 gm 199 527 lin 199 525 gm 199 525 lin 200 80 gm 213 80 lin 200 82 gm 213 82 lin 200 132 gm 213 132 lin 200 134 gm 213 134 lin 200 183 gm 213 183 lin 200 185 gm 213 185 lin 200 254 gm 213 254 lin 200 256 gm 213 256 lin 200 291 gm 213 291 lin 200 293 gm 213 293 lin 200 328 gm 213 328 lin 200 330 gm 213 330 lin 200 365 gm 213 365 lin 200 367 gm 213 367 lin 200 401 gm 213 401 lin 200 403 gm 213 403 lin 200 488 gm 213 488 lin 200 490 gm 213 490 lin 200 525 gm 213 525 lin 200 527 gm 213 527 lin 225 103 gm F 1 setTxMode (11)show 225 149 gm (1699)show 225 203 gm (8205839)show 225 265 gm (4.89)show 225 302 gm (0.44)show 225 339 gm (0.70)show 225 376 gm (0.53)show 225 436 gm (4830)show 225 499 gm (7.50)show 214 82 gm 0 gr 214 82 lin 214 80 gm 214 80 lin 214 83 gm 214 131 lin 214 134 gm 214 134 lin 214 132 gm 214 132 lin 214 135 gm 214 182 lin 214 185 gm 214 185 lin 214 183 gm 214 183 lin 214 186 gm 214 253 lin 214 256 gm 214 256 lin 214 254 gm 214 254 lin 214 257 gm 214 290 lin 214 293 gm 214 293 lin 214 291 gm 214 291 lin 214 294 gm 214 327 lin 214 330 gm 214 330 lin 214 328 gm 214 328 lin 214 331 gm 214 364 lin 214 367 gm 214 367 lin 214 365 gm 214 365 lin 214 368 gm 214 400 lin 214 403 gm 214 403 lin 214 401 gm 214 401 lin 214 404 gm 214 487 lin 214 490 gm 214 490 lin 214 488 gm 214 488 lin 214 491 gm 214 524 lin 214 527 gm 214 527 lin 214 525 gm 214 525 lin 215 80 gm 227 80 lin 215 82 gm 227 82 lin 230 80 gm 230 82 lin 228 80 gm 230 80 lin 228 82 gm 228 82 lin 228 82 lin 228 83 gm 228 131 lin 230 83 gm 230 131 lin 215 132 gm 227 132 lin 215 134 gm 227 134 lin 228 132 gm 228 134 lin 230 132 gm 230 134 lin 228 135 gm 228 182 lin 230 135 gm 230 182 lin 215 183 gm 227 183 lin 215 185 gm 227 185 lin 228 183 gm 228 185 lin 230 183 gm 230 185 lin 228 186 gm 228 253 lin 230 186 gm 230 253 lin 215 254 gm 227 254 lin 215 256 gm 227 256 lin 228 254 gm 228 256 lin 230 254 gm 230 256 lin 228 257 gm 228 290 lin 230 257 gm 230 290 lin 215 291 gm 227 291 lin 215 293 gm 227 293 lin 228 291 gm 228 293 lin 230 291 gm 230 293 lin 228 294 gm 228 327 lin 230 294 gm 230 327 lin 215 328 gm 227 328 lin 215 330 gm 227 330 lin 228 328 gm 228 330 lin 230 328 gm 230 330 lin 228 331 gm 228 364 lin 230 331 gm 230 364 lin 215 365 gm 227 365 lin 215 367 gm 227 367 lin 228 365 gm 228 367 lin 230 365 gm 230 367 lin 228 368 gm 228 400 lin 230 368 gm 230 400 lin 215 401 gm 227 401 lin 215 403 gm 227 403 lin 228 401 gm 228 403 lin 230 401 gm 230 403 lin 228 404 gm 228 487 lin 230 404 gm 230 487 lin 215 488 gm 227 488 lin 215 490 gm 227 490 lin 228 488 gm 228 490 lin 230 488 gm 230 490 lin 228 491 gm 228 524 lin 230 491 gm 230 524 lin 215 525 gm 227 525 lin 215 527 gm 227 527 lin 230 525 gm 230 527 lin 228 527 gm 230 527 lin 228 525 gm 228 525 lin 228 525 lin 242 79 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (Fig.19)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( )show 2 fs bu fc 2 F /|______Times-Italic fnt bn (Young-brothers-wait \(Policy A\))show 276 96 gm 1 fs bu fc 2 F /|______Times-Bold fnt bn (Procs)show 276 145 gm (T\312\(sec\))show 276 200 gm (N\312\(nodes\))show 276 271 gm (S)show 276 308 gm (E)show 276 338 gm (Fpm)show 276 378 gm (SO)show 276 416 gm (SS\312\(nodes/sec\))show 276 502 gm (Sss)show 262 80 gm 0 gr 262 82 lin 262 80 gm 264 80 lin 264 82 gm 264 82 lin 264 82 lin 262 83 gm 262 131 lin 264 83 gm 264 131 lin 262 132 gm 262 134 lin 264 132 gm 264 134 lin 262 135 gm 262 182 lin 264 135 gm 264 182 lin 262 183 gm 262 185 lin 264 183 gm 264 185 lin 262 186 gm 262 253 lin 264 186 gm 264 253 lin 262 254 gm 262 256 lin 264 254 gm 264 256 lin 262 257 gm 262 290 lin 264 257 gm 264 290 lin 262 291 gm 262 293 lin 264 291 gm 264 293 lin 262 294 gm 262 327 lin 264 294 gm 264 327 lin 262 328 gm 262 330 lin 264 328 gm 264 330 lin 262 331 gm 262 364 lin 264 331 gm 264 364 lin 262 365 gm 262 367 lin 264 365 gm 264 367 lin 262 368 gm 262 400 lin 264 368 gm 264 400 lin 262 401 gm 262 403 lin 264 401 gm 264 403 lin 262 404 gm 262 487 lin 264 404 gm 264 487 lin 262 488 gm 262 490 lin 264 488 gm 264 490 lin 262 491 gm 262 524 lin 264 491 gm 264 524 lin 262 525 gm 262 527 lin 264 527 lin 264 525 gm 264 525 lin 264 525 lin 265 80 gm 278 80 lin 265 82 gm 278 82 lin 265 132 gm 278 132 lin 265 134 gm 278 134 lin 265 183 gm 278 183 lin 265 185 gm 278 185 lin 265 254 gm 278 254 lin 265 256 gm 278 256 lin 265 291 gm 278 291 lin 265 293 gm 278 293 lin 265 328 gm 278 328 lin 265 330 gm 278 330 lin 265 365 gm 278 365 lin 265 367 gm 278 367 lin 265 401 gm 278 401 lin 265 403 gm 278 403 lin 265 488 gm 278 488 lin 265 490 gm 278 490 lin 265 525 gm 278 525 lin 265 527 gm 278 527 lin 293 105 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn (1)show 293 149 gm (8301)show 293 203 gm (5347545)show 293 269 gm (---)show 293 306 gm (---)show 293 343 gm (---)show 293 380 gm (---)show 293 439 gm (644)show 293 503 gm (---)show 279 82 gm 0 gr 281 82 lin 279 80 gm 281 80 lin 279 83 gm 279 131 lin 281 83 gm 281 131 lin 279 134 gm 279 134 lin 281 132 gm 281 132 lin 279 132 gm 279 132 lin 281 134 gm 281 134 lin 279 135 gm 279 182 lin 281 135 gm 281 182 lin 279 185 gm 279 185 lin 281 183 gm 281 183 lin 279 183 gm 279 183 lin 281 185 gm 281 185 lin 279 186 gm 279 253 lin 281 186 gm 281 253 lin 279 256 gm 279 256 lin 281 254 gm 281 254 lin 279 254 gm 279 254 lin 281 256 gm 281 256 lin 279 257 gm 279 290 lin 281 257 gm 281 290 lin 279 293 gm 279 293 lin 281 291 gm 281 291 lin 279 291 gm 279 291 lin 281 293 gm 281 293 lin 279 294 gm 279 327 lin 281 294 gm 281 327 lin 279 330 gm 279 330 lin 281 328 gm 281 328 lin 279 328 gm 279 328 lin 281 330 gm 281 330 lin 279 331 gm 279 364 lin 281 331 gm 281 364 lin 279 367 gm 279 367 lin 281 365 gm 281 365 lin 279 365 gm 279 365 lin 281 367 gm 281 367 lin 279 368 gm 279 400 lin 281 368 gm 281 400 lin 279 403 gm 279 403 lin 281 401 gm 281 401 lin 279 401 gm 279 401 lin 281 403 gm 281 403 lin 279 404 gm 279 487 lin 281 404 gm 281 487 lin 279 490 gm 279 490 lin 281 488 gm 281 488 lin 279 488 gm 279 488 lin 281 490 gm 281 490 lin 279 491 gm 279 524 lin 281 491 gm 281 524 lin 279 527 gm 281 527 lin 279 525 gm 281 525 lin 282 80 gm 295 80 lin 282 82 gm 295 82 lin 282 132 gm 295 132 lin 282 134 gm 295 134 lin 282 183 gm 295 183 lin 282 185 gm 295 185 lin 282 254 gm 295 254 lin 282 256 gm 295 256 lin 282 291 gm 295 291 lin 282 293 gm 295 293 lin 282 328 gm 295 328 lin 282 330 gm 295 330 lin 282 365 gm 295 365 lin 282 367 gm 295 367 lin 282 401 gm 295 401 lin 282 403 gm 295 403 lin 282 488 gm 295 488 lin 282 490 gm 295 490 lin 282 525 gm 295 525 lin 282 527 gm 295 527 lin 308 105 gm F 1 setTxMode (3)show 308 149 gm (4629)show 308 203 gm (6476838)show 308 265 gm (1.79)show 308 302 gm (0.60)show 308 339 gm (0.84)show 308 376 gm (0.21)show 308 436 gm (1399)show 308 499 gm (2.17)show 296 82 gm 0 gr 296 82 lin 296 80 gm 296 80 lin 296 83 gm 296 131 lin 296 134 gm 296 134 lin 296 132 gm 296 132 lin 296 135 gm 296 182 lin 296 185 gm 296 185 lin 296 183 gm 296 183 lin 296 186 gm 296 253 lin 296 256 gm 296 256 lin 296 254 gm 296 254 lin 296 257 gm 296 290 lin 296 293 gm 296 293 lin 296 291 gm 296 291 lin 296 294 gm 296 327 lin 296 330 gm 296 330 lin 296 328 gm 296 328 lin 296 331 gm 296 364 lin 296 367 gm 296 367 lin 296 365 gm 296 365 lin 296 368 gm 296 400 lin 296 403 gm 296 403 lin 296 401 gm 296 401 lin 296 404 gm 296 487 lin 296 490 gm 296 490 lin 296 488 gm 296 488 lin 296 491 gm 296 524 lin 296 527 gm 296 527 lin 296 525 gm 296 525 lin 297 80 gm 310 80 lin 297 82 gm 310 82 lin 297 132 gm 310 132 lin 297 134 gm 310 134 lin 297 183 gm 310 183 lin 297 185 gm 310 185 lin 297 254 gm 310 254 lin 297 256 gm 310 256 lin 297 291 gm 310 291 lin 297 293 gm 310 293 lin 297 328 gm 310 328 lin 297 330 gm 310 330 lin 297 365 gm 310 365 lin 297 367 gm 310 367 lin 297 401 gm 310 401 lin 297 403 gm 310 403 lin 297 488 gm 310 488 lin 297 490 gm 310 490 lin 297 525 gm 310 525 lin 297 527 gm 310 527 lin 323 105 gm F 1 setTxMode (5)show 323 149 gm (2798)show 323 203 gm (7280335)show 323 265 gm (2.97)show 323 302 gm (0.59)show 323 339 gm (0.88)show 323 376 gm (0.36)show 323 436 gm (2602)show 323 499 gm (4.04)show 311 82 gm 0 gr 311 82 lin 311 80 gm 311 80 lin 311 83 gm 311 131 lin 311 134 gm 311 134 lin 311 132 gm 311 132 lin 311 135 gm 311 182 lin 311 185 gm 311 185 lin 311 183 gm 311 183 lin 311 186 gm 311 253 lin 311 256 gm 311 256 lin 311 254 gm 311 254 lin 311 257 gm 311 290 lin 311 293 gm 311 293 lin 311 291 gm 311 291 lin 311 294 gm 311 327 lin 311 330 gm 311 330 lin 311 328 gm 311 328 lin 311 331 gm 311 364 lin 311 367 gm 311 367 lin 311 365 gm 311 365 lin 311 368 gm 311 400 lin 311 403 gm 311 403 lin 311 401 gm 311 401 lin 311 404 gm 311 487 lin 311 490 gm 311 490 lin 311 488 gm 311 488 lin 311 491 gm 311 524 lin 311 527 gm 311 527 lin 311 525 gm 311 525 lin 312 80 gm 325 80 lin 312 82 gm 325 82 lin 312 132 gm 325 132 lin 312 134 gm 325 134 lin 312 183 gm 325 183 lin 312 185 gm 325 185 lin 312 254 gm 325 254 lin 312 256 gm 325 256 lin 312 291 gm 325 291 lin 312 293 gm 325 293 lin 312 328 gm 325 328 lin 312 330 gm 325 330 lin 312 365 gm 325 365 lin 312 367 gm 325 367 lin 312 401 gm 325 401 lin 312 403 gm 325 403 lin 312 488 gm 325 488 lin 312 490 gm 325 490 lin 312 525 gm 325 525 lin 312 527 gm 325 527 lin 338 105 gm F 1 setTxMode (7)show 338 149 gm (2223)show 338 203 gm (8133582)show 338 265 gm (3.73)show 338 302 gm (0.53)show 338 339 gm (0.89)show 338 376 gm (0.52)show 338 436 gm (3659)show 338 499 gm (5.68)show 326 82 gm 0 gr 326 82 lin 326 80 gm 326 80 lin 326 83 gm 326 131 lin 326 134 gm 326 134 lin 326 132 gm 326 132 lin 326 135 gm 326 182 lin 326 185 gm 326 185 lin 326 183 gm 326 183 lin 326 186 gm 326 253 lin 326 256 gm 326 256 lin 326 254 gm 326 254 lin 326 257 gm 326 290 lin 326 293 gm 326 293 lin 326 291 gm 326 291 lin 326 294 gm 326 327 lin 326 330 gm 326 330 lin 326 328 gm 326 328 lin 326 331 gm 326 364 lin 326 367 gm 326 367 lin 326 365 gm 326 365 lin 326 368 gm 326 400 lin 326 403 gm 326 403 lin 326 401 gm 326 401 lin 326 404 gm 326 487 lin 326 490 gm 326 490 lin 326 488 gm 326 488 lin 326 491 gm 326 524 lin 326 527 gm 326 527 lin 326 525 gm 326 525 lin 327 80 gm 340 80 lin 327 82 gm 340 82 lin 327 132 gm 340 132 lin 327 134 gm 340 134 lin 327 183 gm 340 183 lin 327 185 gm 340 185 lin 327 254 gm 340 254 lin 327 256 gm 340 256 lin 327 291 gm 340 291 lin 327 293 gm 340 293 lin 327 328 gm 340 328 lin 327 330 gm 340 330 lin 327 365 gm 340 365 lin 327 367 gm 340 367 lin 327 401 gm 340 401 lin 327 403 gm 340 403 lin 327 488 gm 340 488 lin 327 490 gm 340 490 lin 327 525 gm 340 525 lin 327 527 gm 340 527 lin 353 105 gm F 1 setTxMode (9)show 353 149 gm (1972)show 353 203 gm (8541944)show 353 265 gm (4.21)show 353 302 gm (0.47)show 353 339 gm (0.89)show 353 376 gm (0.60)show 353 436 gm (4332)show 353 499 gm (6.72)show 341 82 gm 0 gr 341 82 lin 341 80 gm 341 80 lin 341 83 gm 341 131 lin 341 134 gm 341 134 lin 341 132 gm 341 132 lin 341 135 gm 341 182 lin 341 185 gm 341 185 lin 341 183 gm 341 183 lin 341 186 gm 341 253 lin 341 256 gm 341 256 lin 341 254 gm 341 254 lin 341 257 gm 341 290 lin 341 293 gm 341 293 lin 341 291 gm 341 291 lin 341 294 gm 341 327 lin 341 330 gm 341 330 lin 341 328 gm 341 328 lin 341 331 gm 341 364 lin 341 367 gm 341 367 lin 341 365 gm 341 365 lin 341 368 gm 341 400 lin 341 403 gm 341 403 lin 341 401 gm 341 401 lin 341 404 gm 341 487 lin 341 490 gm 341 490 lin 341 488 gm 341 488 lin 341 491 gm 341 524 lin 341 527 gm 341 527 lin 341 525 gm 341 525 lin 342 80 gm 355 80 lin 342 82 gm 355 82 lin 342 132 gm 355 132 lin 342 134 gm 355 134 lin 342 183 gm 355 183 lin 342 185 gm 355 185 lin 342 254 gm 355 254 lin 342 256 gm 355 256 lin 342 291 gm 355 291 lin 342 293 gm 355 293 lin 342 328 gm 355 328 lin 342 330 gm 355 330 lin 342 365 gm 355 365 lin 342 367 gm 355 367 lin 342 401 gm 355 401 lin 342 403 gm 355 403 lin 342 488 gm 355 488 lin 342 490 gm 355 490 lin 342 525 gm 355 525 lin 342 527 gm 355 527 lin 368 103 gm F 1 setTxMode (11)show 368 149 gm (1663)show 368 203 gm (8689459)show 368 265 gm (4.99)show 368 302 gm (0.45)show 368 339 gm (0.89)show 368 376 gm (0.62)show 368 436 gm (5225)show 368 499 gm (8.11)show 356 82 gm 0 gr 356 82 lin 356 80 gm 356 80 lin 356 83 gm 356 131 lin 356 134 gm 356 134 lin 356 132 gm 356 132 lin 356 135 gm 356 182 lin 356 185 gm 356 185 lin 356 183 gm 356 183 lin 356 186 gm 356 253 lin 356 256 gm 356 256 lin 356 254 gm 356 254 lin 356 257 gm 356 290 lin 356 293 gm 356 293 lin 356 291 gm 356 291 lin 356 294 gm 356 327 lin 356 330 gm 356 330 lin 356 328 gm 356 328 lin 356 331 gm 356 364 lin 356 367 gm 356 367 lin 356 365 gm 356 365 lin 356 368 gm 356 400 lin 356 403 gm 356 403 lin 356 401 gm 356 401 lin 356 404 gm 356 487 lin 356 490 gm 356 490 lin 356 488 gm 356 488 lin 356 491 gm 356 524 lin 356 527 gm 356 527 lin 356 525 gm 356 525 lin 357 80 gm 370 80 lin 357 82 gm 370 82 lin 373 80 gm 373 82 lin 371 80 gm 373 80 lin 371 82 gm 371 82 lin 371 82 lin 371 83 gm 371 131 lin 373 83 gm 373 131 lin 357 132 gm 370 132 lin 357 134 gm 370 134 lin 371 132 gm 371 134 lin 373 132 gm 373 134 lin 371 135 gm 371 182 lin 373 135 gm 373 182 lin 357 183 gm 370 183 lin 357 185 gm 370 185 lin 371 183 gm 371 185 lin 373 183 gm 373 185 lin 371 186 gm 371 253 lin 373 186 gm 373 253 lin 357 254 gm 370 254 lin 357 256 gm 370 256 lin 371 254 gm 371 256 lin 373 254 gm 373 256 lin 371 257 gm 371 290 lin 373 257 gm 373 290 lin 357 291 gm 370 291 lin 357 293 gm 370 293 lin 371 291 gm 371 293 lin 373 291 gm 373 293 lin 371 294 gm 371 327 lin 373 294 gm 373 327 lin 357 328 gm 370 328 lin 357 330 gm 370 330 lin 371 328 gm 371 330 lin 373 328 gm 373 330 lin 371 331 gm 371 364 lin 373 331 gm 373 364 lin 357 365 gm 370 365 lin 357 367 gm 370 367 lin 371 365 gm 371 367 lin 373 365 gm 373 367 lin 371 368 gm 371 400 lin 373 368 gm 373 400 lin 357 401 gm 370 401 lin 357 403 gm 370 403 lin 371 401 gm 371 403 lin 373 401 gm 373 403 lin 371 404 gm 371 487 lin 373 404 gm 373 487 lin 357 488 gm 370 488 lin 357 490 gm 370 490 lin 371 488 gm 371 490 lin 373 488 gm 373 490 lin 371 491 gm 371 524 lin 373 491 gm 373 524 lin 357 525 gm 370 525 lin 357 527 gm 370 527 lin 373 525 gm 373 527 lin 371 527 gm 373 527 lin 371 525 gm 371 525 lin 371 525 lin 385 79 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (Fig.20)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( )show 2 fs bu fc 2 F /|______Times-Italic fnt bn (Young-brothers-wait \(Policy B\))show 401 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.80612 0. 32 0.08061 0.(These tables show several differences, although the policies are similar. Policy A gives a smaller)awidthshow 412 79 gm 0.13977 0. 32 0.01397 0.(search overhead, thanks to the signature tree; moreover, using less processors policy A is better than)awidthshow 423 79 gm 1.55426 0. 32 0.15542 0.(B. However, the production factor in A deteriorates with more processors, because the global)awidthshow 434 79 gm 0.20507 0. 32 0.02050 0.(condition it uses reduces the response time for each new task, even if there are "often" idle workers.)awidthshow 445 79 gm 0.20172 0. 32 0.02017 0.(On the other hand, policy B increments the average number of tasks in the agenda, and it lowers the)awidthshow 456 79 gm 0.15075 0. 32 0.01507 0.(coupling between the master and the workers. With 11 processors, we have a high production factor)awidthshow 467 79 gm 0.84869 0. 32 0.08486 0.(\(89%\). This algorithm results in a finer splitting and higher communication overhead due to task)awidthshow 478 79 gm -0.00103 0.(distribution and collection of results. Let us try to analyze such an overhead. Look at the F)ashow 9 fz bu fc 2 F /|______Times-Roman fnt bn (pm)show 11 fz bu fc 2 F /|______Times-Roman fnt bn ( column)show 489 79 gm 0.65643 0. 32 0.06564 0.(in Fig.21: such values include also communication overhead. Thus, we should split F)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.20443 0.(pm)ashow 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.37826 0. 32 0.03782 0.( into F)awidthshow 9 fz bu fc 2 F /|______Times-Roman fnt bn 0.25767 0.(pmr)ashow 500 79 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn (\(real productivity\) e OC \(communication overhead\):)show 529 98 gm 1 fs 10 fz bu fc 2 F /|______Times-Bold fnt bn (Procs)show 529 146 gm (Fpm)show 529 181 gm (Fpmr)show 529 223 gm (OC)show 515 80 gm 0 gr 515 82 lin 515 80 gm 517 80 lin 517 82 gm 517 82 lin 517 82 lin 515 83 gm 515 135 lin 517 83 gm 517 135 lin 515 136 gm 515 138 lin 517 136 gm 517 138 lin 515 139 gm 515 172 lin 517 139 gm 517 172 lin 515 173 gm 515 175 lin 517 173 gm 517 175 lin 515 176 gm 515 209 lin 517 176 gm 517 209 lin 515 210 gm 515 212 lin 517 210 gm 517 212 lin 515 213 gm 515 246 lin 517 213 gm 517 246 lin 515 247 gm 515 249 lin 517 249 lin 517 247 gm 517 247 lin 517 247 lin 518 80 gm 531 80 lin 518 82 gm 531 82 lin 518 136 gm 531 136 lin 518 138 gm 531 138 lin 518 173 gm 531 173 lin 518 175 gm 531 175 lin 518 210 gm 531 210 lin 518 212 gm 531 212 lin 518 247 gm 531 247 lin 518 249 gm 531 249 lin 546 107 gm F 1 setTxMode 0 fs bu fc 2 F /|______Times-Roman fnt bn (3)show 546 147 gm (0.85)show 546 184 gm (0.84)show 546 221 gm (0.01)show 532 82 gm 0 gr 534 82 lin 532 80 gm 534 80 lin 532 83 gm 532 135 lin 534 83 gm 534 135 lin 532 138 gm 532 138 lin 534 136 gm 534 136 lin 532 136 gm 532 136 lin 534 138 gm 534 138 lin 532 139 gm 532 172 lin 534 139 gm 534 172 lin 532 175 gm 532 175 lin 534 173 gm 534 173 lin 532 173 gm 532 173 lin 534 175 gm 534 175 lin 532 176 gm 532 209 lin 534 176 gm 534 209 lin 532 212 gm 532 212 lin 534 210 gm 534 210 lin 532 210 gm 532 210 lin 534 212 gm 534 212 lin 532 213 gm 532 246 lin 534 213 gm 534 246 lin 532 249 gm 534 249 lin 532 247 gm 534 247 lin 535 80 gm 548 80 lin 535 82 gm 548 82 lin 535 136 gm 548 136 lin 535 138 gm 548 138 lin 535 173 gm 548 173 lin 535 175 gm 548 175 lin 535 210 gm 548 210 lin 535 212 gm 548 212 lin 535 247 gm 548 247 lin 535 249 gm 548 249 lin 561 107 gm F 1 setTxMode (5)show 561 147 gm (0.88)show 561 184 gm (0.80)show 561 221 gm (0.08)show 549 82 gm 0 gr 549 82 lin 549 80 gm 549 80 lin 549 83 gm 549 135 lin 549 138 gm 549 138 lin 549 136 gm 549 136 lin 549 139 gm 549 172 lin 549 175 gm 549 175 lin 549 173 gm 549 173 lin 549 176 gm 549 209 lin 549 212 gm 549 212 lin 549 210 gm 549 210 lin 549 213 gm 549 246 lin 549 249 gm 549 249 lin 549 247 gm 549 247 lin 550 80 gm 563 80 lin 550 82 gm 563 82 lin 550 136 gm 563 136 lin 550 138 gm 563 138 lin 550 173 gm 563 173 lin 550 175 gm 563 175 lin 550 210 gm 563 210 lin 550 212 gm 563 212 lin 550 247 gm 563 247 lin 550 249 gm 563 249 lin 576 107 gm F 1 setTxMode (7)show 576 147 gm (0.89)show 576 184 gm (0.80)show 576 221 gm (0.09)show 564 82 gm 0 gr 564 82 lin 564 80 gm 564 80 lin 564 83 gm 564 135 lin 564 138 gm 564 138 lin 564 136 gm 564 136 lin 564 139 gm 564 172 lin 564 175 gm 564 175 lin 564 173 gm 564 173 lin 564 176 gm 564 209 lin 564 212 gm 564 212 lin 564 210 gm 564 210 lin 564 213 gm 564 246 lin 564 249 gm 564 249 lin 564 247 gm 564 247 lin 565 80 gm 578 80 lin 565 82 gm 578 82 lin 565 136 gm 578 136 lin 565 138 gm 578 138 lin 565 173 gm 578 173 lin 565 175 gm 578 175 lin 565 210 gm 578 210 lin 565 212 gm 578 212 lin 565 247 gm 578 247 lin 565 249 gm 578 249 lin 591 107 gm F 1 setTxMode (9)show 591 147 gm (0.89)show 591 184 gm (0.75)show 591 221 gm (0.14)show 579 82 gm 0 gr 579 82 lin 579 80 gm 579 80 lin 579 83 gm 579 135 lin 579 138 gm 579 138 lin 579 136 gm 579 136 lin 579 139 gm 579 172 lin 579 175 gm 579 175 lin 579 173 gm 579 173 lin 579 176 gm 579 209 lin 579 212 gm 579 212 lin 579 210 gm 579 210 lin 579 213 gm 579 246 lin 579 249 gm 579 249 lin 579 247 gm 579 247 lin 580 80 gm 593 80 lin 580 82 gm 593 82 lin 580 136 gm 593 136 lin 580 138 gm 593 138 lin 580 173 gm 593 173 lin 580 175 gm 593 175 lin 580 210 gm 593 210 lin 580 212 gm 593 212 lin 580 247 gm 593 247 lin 580 249 gm 593 249 lin 606 105 gm F 1 setTxMode (11)show 606 147 gm (0.89)show 606 184 gm (0.73)show 606 221 gm (0.16)show 594 82 gm 0 gr 594 82 lin 594 80 gm 594 80 lin 594 83 gm 594 135 lin 594 138 gm 594 138 lin 594 136 gm 594 136 lin 594 139 gm 594 172 lin 594 175 gm 594 175 lin 594 173 gm 594 173 lin 594 176 gm 594 209 lin 594 212 gm 594 212 lin 594 210 gm 594 210 lin 594 213 gm 594 246 lin 594 249 gm 594 249 lin 594 247 gm 594 247 lin 595 80 gm 608 80 lin 595 82 gm 608 82 lin 611 80 gm 611 82 lin 609 80 gm 611 80 lin 609 82 gm 609 82 lin 609 82 lin 609 83 gm 609 135 lin 611 83 gm 611 135 lin 595 136 gm 608 136 lin 595 138 gm 608 138 lin 609 136 gm 609 138 lin 611 136 gm 611 138 lin 609 139 gm 609 172 lin 611 139 gm 611 172 lin 595 173 gm 608 173 lin 595 175 gm 608 175 lin 609 173 gm 609 175 lin 611 173 gm 611 175 lin 609 176 gm 609 209 lin 611 176 gm 611 209 lin 595 210 gm 608 210 lin 595 212 gm 608 212 lin 609 210 gm 609 212 lin 611 210 gm 611 212 lin 609 213 gm 609 246 lin 611 213 gm 611 246 lin 595 247 gm 608 247 lin 595 249 gm 608 249 lin 611 247 gm 611 249 lin 609 249 gm 611 249 lin 609 247 gm 609 247 lin 609 247 lin 623 79 gm F 1 setTxMode 1 fs bu fc 2 F /|______Times-Bold fnt bn (Fig.21)show 0 fs bu fc 2 F /|______Times-Roman fnt bn ( )show 2 fs bu fc 2 F /|______Times-Italic fnt bn (Policy B: analyizing the average production factor)show 639 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 2.32254 0. 32 0.23225 0.(Such a table shows that the cost to be paid for communication overhead on a network of)awidthshow 650 79 gm (workstations is high.)show 680 79 gm 1 fs 12 fz bu fc 2 F /|______Times-Bold fnt bn (6. Conclusions)show 693 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.09750 0. 32 0.00975 0.(We have compared a number of parallel search algorithms in the domain of chess. We used Linda to)awidthshow 704 79 gm 2.65197 0. 32 0.26519 0.(develop two basic programs, one for static splitting and one for dynamic splitting. Their)awidthshow 715 79 gm 1.17568 0. 32 0.11756 0.(performances were progressively improved, especially using democratic cooperation with a low)awidthshow 726 79 gm 0.44967 0. 32 0.04496 0.(number of processors. For all algorithms we have sistematically measured the speedup S. We have)awidthshow 737 79 gm 0.63659 0. 32 0.06365 0.(seen that the theoretically optimum speedup S=N with N processors is impossible to reach for the)awidthshow 748 79 gm (following reasons:)show F T cp %%Page: ? 19 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 336 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Helvetica fnt bn (A Comparison of Parallel Search Algorithms)show 773 79 gm (UBLCS-94-14)show 773 514 gm (17)show 118 88 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn (\245\312commmunication overhead, given by messages betwen processors;)show 131 88 gm (\245\312search overhead, given by duplication of subtree evaluation;)show 144 88 gm (\245\312synchronisation overhead, given by bad load balancing.)show 156 79 gm 0.64361 0. 32 0.06436 0.(The most annoying problem is the coupling among these overheads: if we tried to reduce one, we)awidthshow 167 79 gm 0.73684 0. 32 0.07368 0.(got always an increase in another. For instance, the algorithm with dynamic splitting of the game)awidthshow 178 79 gm 0.86013 0. 32 0.08601 0.(tree top level \(Fig.15\) gives the best load balancing \(Fpm=90% with 11 processors\), but also the)awidthshow 189 79 gm (worst search overhead \(SO=108% with 11 processors\).)show 200 79 gm 0.15335 0. 32 0.01533 0.(Thus, we searched for a tradeoff among the overheads. Our results say that the best results are given)awidthshow 211 79 gm 1.15768 0. 32 0.11576 0.(by PVSplit combined either with score sharing \(S=5.57 with 11 processors; see Fig.13\) or with)awidthshow 222 79 gm (dynamic distribution \(S=5.58 with 11 processors; see Fig.16\).)show 233 79 gm 1.33804 0. 32 0.13380 0.(Our results can easily be compared with results obtained by other researchers. For instance, in)awidthshow 244 79 gm 0.79193 0. 32 0.07919 0.([MOS86] a speedup of 3.66 with 5 workstations is reported; such a measure was obtained with a)awidthshow 255 79 gm 0.22323 0. 32 0.02232 0.(depth of 7 plies on the Bratko-Kopec test; with a shallower depth \(5 plies\) we got a speedup of 3.49)awidthshow 266 79 gm 1.10260 0. 32 0.11026 0.(\(3.75 with score sharing\). In [Sch89] a speedup of 4.78 with 7 processors, depth of 7 plies was)awidthshow 277 79 gm 0.07385 0. 32 0.00738 0.(obtained for DPVSplit; we got a speedup of 4.54 \(depth = 5 plies\). These results seem to say that the)awidthshow 288 79 gm 1.30981 0. 32 0.13098 0.(use of the Linda programming model does not introduce any special overhead for this class of)awidthshow 299 79 gm (programs.)show 310 79 gm 0.55175 0. 32 0.05517 0.(On the other hand, we got bad comparison results for algorithms based on dynamic distribution of)awidthshow 321 79 gm 2.16812 0. 32 0.21681 0.(search. However, the problem seems to be the hardware architecture, not the programming)awidthshow 332 79 gm (environment; in fact, we found the following results in literature:)show 345 88 gm 10 fz bu fc 2 F /|______Times-Roman fnt bn 0.34454 0. 32 0.03445 0.(\245\312[Eli90] reports that the program Oracol, based on dynamic splitting and written in Orca, gets a maximum)awidthshow 356 101 gm (speedup of 5.5 on a multiprocessor with shared memory and 10 processors.)show 369 88 gm 1.61331 0. 32 0.16133 0.(\245\312[FMM92] presents a dynamic algorithm based on "young-brothers-wait". On a transputer with 256)awidthshow 380 101 gm (processors, the authors report a surprising speedup of 126 \(depth 8-plies\).)show 391 79 gm 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.74722 0. 32 0.07472 0.(These results suggest that dynamic splitting algorithms can offer good performances, but only on)awidthshow 402 79 gm 0.29296 0. 32 0.02929 0.(shared memory or on massive parallel systems where communication and fine-grain parallelism are)awidthshow 413 79 gm 0.30899 0. 32 0.03089 0.(cheap. It would be interesting to test out general dynamic splitting algorithm on these architectures.)awidthshow 424 79 gm 1.09130 0. 32 0.10913 0.(Also, it would be interesting to verify in massively parallel machines the asyntotic convergence)awidthshow 435 79 gm (postulated in [MOS86] for static splitting methods .)show 457 79 gm 1 fs bu fc 2 F /|______Times-Bold fnt bn 0.00860 0.(Acknowledgements)ashow 457 170 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn 3.80035 0. 32 0.38003 0.(. This paper has been partially supported by ESPRIT BRA Project)awidthshow 468 79 gm 0.03295 0. 32 0.00329 0.(BROADCAST and by Italian CNR.)awidthshow F T cp %%Page: ? 20 op 30 28 811 566 fr 0 0 xl 1 1 pen 0 0 gm (nc 0 0 0 0 6 rc)kp 91 476 gm (nc 30 28 811 566 6 rc)kp F 1 setTxMode 0 fs 10 fz bu fc 2 F /|______Helvetica fnt bn (Bibliography)show 773 79 gm (UBLCS-94-14)show 773 514 gm (18)show 134 79 gm 1 fs 12 fz bu fc 2 F /|______Times-Bold fnt bn (Bibliography)show 158 79 gm 0 fs 11 fz bu fc 2 F /|______Times-Roman fnt bn 0.00982 0.([ABD82])ashow 158 130 gm 0.88424 0. 32 0.08842 0.(S.Akl, D.Barnard, R.Doran, "Design, Analysis, and Implementation of a Parallel Tree)awidthshow 169 130 gm 0.81619 0. 32 0.08161 0.(Search Algorithm", )awidthshow 169 221 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.82031 0. 32 0.08203 0.(IEEE Transactions on Pattern Analysis and Machine Intelligence,)awidthshow 180 130 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn (4\(2\), \(1982\), 192-203.)show 191 79 gm 0.11459 0. 32 0.01145 0.([BalvRe86] H.Bal, R.vanRenesse, "A summary of parallel alpha-beta search results", )awidthshow 2 fs bu fc 2 F /|______Times-Italic fnt bn 0.16403 0. 32 0.01640 0.(ICCA Journal)awidthshow 191 520 gm 0 fs bu fc 2 F /|______Times-Roman fnt bn (,)show 202 130 gm (\(Sep.1986\), 146-149.)show 213 79 gm 0.00852 0.([Bau78])ashow 213 130 gm 0.95748 0. 32 0.09574 0.(G.Baudet, "The design and analysis of algorithms for asynchronous multiprocessors",)awidthshow 224 130 gm (Ph.D. Thesis, CS Dept., Carnegie-Mellon Univ., \(Apr.1978\).)show 235 79 gm 1.93359 0. 32 0.19335 0.([BraKop82] I.Bratko, D.Kopec, "The Bratko-Kopec experiment: a comparison of human and)awidthshow 246 130 gm 1.90719 0. 32 0.19071 0.(computer performance in chess", )awidthshow 2 fs bu fc 2 F /|______Times-Italic fnt bn 1.87927 0. 32 0.18792 0.(Advances in Computer Chess 3)awidthshow 0 fs bu fc 2 F /|______Times-Roman fnt bn 1.51840 0. 32 0.15184 0.(, M Clarke \(Ed.\),)awidthshow 257 130 gm (\(1982\), 57)show 257 175 gm (-72, Pergamon Press.)show 268 79 gm 0.81268 0. 32 0.08126 0.([CarGel90] N.Carriero, D.Gelernter, )awidthshow 268 247 gm 2 fs bu fc 2 F /|______Times-Italic fnt bn 1.04995 0. 32 0.10499 0.(How to write parallel programs. 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