From 10acef9e6f2d1f56a39c7f4b9ccf4b4be6f8bed7 Mon Sep 17 00:00:00 2001 From: Scott Gasch Date: Wed, 1 Jun 2016 19:04:57 -0700 Subject: A bunch of chess-related papers. --- parallel/ciancarini94comparison.ps | 24943 +++++++++++++++++++++++++++++++++++ 1 file changed, 24943 insertions(+) create mode 100755 parallel/ciancarini94comparison.ps (limited to 'parallel/ciancarini94comparison.ps') diff --git a/parallel/ciancarini94comparison.ps b/parallel/ciancarini94comparison.ps new file mode 100755 index 0000000..ec7f5d1 --- /dev/null +++ b/parallel/ciancarini94comparison.ps @@ -0,0 +1,24943 @@ +%!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 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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 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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 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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 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/|______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 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+(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 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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 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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 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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 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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 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+(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 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+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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Beal \(Ed.\), \(1991\), 1)show +345 330 gm +(-27.)show +356 79 gm +0.01040 0.([FMM92])ashow +356 130 gm +1.51596 0. 32 0.15159 0.(R.Feldmann, P.Mysliwietz, B.Monien, "Experiments with a Fully-Distributed Chess)awidthshow +367 130 gm +1.80343 0. 32 0.18034 0.(Program", )awidthshow +367 181 gm +2 fs +bu fc +2 F /|______Times-Italic fnt +bn +1.83212 0. 32 0.18321 0.(Heuristic Programming in AI)awidthshow +367 321 gm +0 fs +bu fc +2 F /|______Times-Roman fnt +bn +1.69158 0. 32 0.16915 0.(, J.VanDenHerik and\312V.Allis \(Eds.\), Hellis)awidthshow +378 130 gm +(Horwood, \(1992\), 72-87.)show +389 79 gm +0.00732 0.([FelOtt88])ashow +389 130 gm +2.39242 0. 32 0.23924 0.(E.Felten, S.Otto, "A Highly Parallel Chess Program", )awidthshow +2 fs +bu fc +2 F /|______Times-Italic fnt +bn +2.52624 0. 32 0.25262 0.(Proc. of the International)awidthshow +400 130 gm +(Conference on Fifth Generation Computer Systems)show +400 356 gm +0 fs +bu fc +2 F /|______Times-Roman fnt +bn +(, \(1988\), 1001-1009.)show +411 79 gm +0.00732 0.([FisFin80])ashow +411 130 gm +0.42098 0. 32 0.04209 0.(J.Fishburn, R.Finkel, "Parallelism in Alpha-Beta Search on Arachne", Technical Report)awidthshow +422 130 gm +(394, CS. 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