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%%EndProlog
%%BeginSetup
%%Feature: *Resolution 300dpi
TeXDict begin
%%EndSetup
%%Page: 1 1
1 0 bop 591 369 a Fv(APHID)22 b(Game-T)-6 b(ree)22 b(Searc)n(h)516
490 y Fu(Mark)16 b(G.)g(Bro)q(c)o(kington,)g Ft(br)n(o)n([email protected])n
(erta.c)n(a)504 548 y Fu(Jonathan)i(Sc)o(hae\013er,)d
Ft([email protected])n(erta.c)n(a)685 606 y Fs(Departmen)o(t)f(of)f
(Computing)h(Science)797 664 y(Univ)o(ersit)o(y)h(of)d(Alb)q(erta)727
722 y(Edmon)o(ton,)i(Alb)q(erta)g(T6G)f(2H1)911 780 y(Canada)828
878 y Fu(June)k(13,)f(1996)890 1017 y Fr(Abstract)161
1073 y Fs(This)g(pap)q(er)h(in)o(tro)q(duces)g(the)e(APHID)g(\(Async)o
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(ening\))i(game-)104 1118 y(tree)13 b(searc)o(h)g(algorithm.)19
b(An)13 b(APHID)g(searc)o(h)h(is)f(con)o(trolled)j(b)o(y)d(a)g(master)g
(and)h(a)f(series)h(of)f(sla)o(v)o(e)h(pro)q(cessors.)k(The)104
1164 y(master)d(searc)o(hes)g(the)g(\014rst)g Fq(d)551
1148 y Fp(0)576 1164 y Fs(ply)h(of)e(the)h(game-tree)g(rep)q(eatedly)m
(.)24 b(The)14 b(sla)o(v)o(es)i(are)f(resp)q(onsible)i(for)e(the)g(b)q
(ottom)104 1210 y(plies)k(of)f(the)f(game-tree.)32 b(The)17
b(sla)o(v)o(es)i(async)o(hronously)i(read)d(w)o(ork)g(lists)h(from)e
(the)h(master)g(and)g(return)h(score)104 1255 y(information)g(to)d(the)
h(master.)29 b(The)17 b(master)g(uses)g(the)g(returned)h(score)f
(information)i(to)e(generate)g(appro)o(ximate)104 1301
y(minimax)e(v)n(alues,)f(un)o(til)g(all)h(of)d(the)i(required)g(score)f
(information)j(is)d(a)o(v)n(ailable.)161 1346 y(APHID)e(has)g(b)q(een)g
(programmed)g(as)g(an)g(easy)g(to)f(implemen)o(t,)j(game-indep)q(enden)
o(t)g Fq(\013\014)f Fs(library)m(,)g(and)f(w)o(as)g(imple-)104
1392 y(men)o(ted)g(in)o(to)h(a)g(c)o(hess)f(program)h(with)g(one)f(da)o
(y)h(of)f(programming)i(e\013ort.)k(APHID)11 b(yields)i(reasonable)g(p)
q(erformance)104 1438 y(on)e(a)h(net)o(w)o(ork)f(of)g(w)o(orkstations,)
i(an)f(arc)o(hitecture)h(where)e(it)h(is)g(extremely)g(di\016cult)h(to)
f(use)f(a)h(shared)g(transp)q(osition)104 1483 y(table)i(e\013fectiv)o
(ely)m(.)0 1619 y Fo(1)69 b(In)n(tro)r(duction)0 1722
y Fn(The)18 b(alpha-b)q(eta)f(\()p Fm(\013\014)r Fn(\))h(minim)o(ax)c
(tree)19 b(searc)o(h)f(algorithm)d(has)j(pro)o(v)o(en)f(to)g(b)q(e)h(a)
f(di\016cult)g(algorithm)e(to)i(parallelize.)0 1785 y(Although)e(sim)o
(ulations)e(predict)k(excellen)o(t)f(parallel)f(p)q(erformance,)g(man)o
(y)f(of)h(these)i(results)g(are)f(based)h(on)e(an)h(unrea-)0
1847 y(sonable)c(set)h(of)e(assumptions.)17 b(In)12 b(practice,)h(kno)o
(wing)e(where)i(to)f(initiate)f(parallel)g(activit)o(y)g(is)h
(di\016cult)g(since)h(the)f(result)0 1909 y(of)18 b(searc)o(hing)g(one)
h(no)q(de)f(at)g(a)g(branc)o(h)h(ma)o(y)d(ob)o(viate)i(the)h(parallel)e
(w)o(ork)g(of)h(the)h(other)g(branc)o(hes)g(\(a)f(so-called)g
Fl(cut-)0 1972 y(o\013)p Fn(\).)h(In)14 b(real-w)o(orld)f(implemen)o
(tations,)d(suc)o(h)15 b(as)f(for)g(high-p)q(erformance)f(c)o(hess,)i
(c)o(hec)o(k)o(ers)h(and)d(Othello)h(game-pla)o(ying)0
2034 y(programs,)e(the)j(programs)d(su\013er)k(from)c(three)j(ma)r(jor)
d(sources)k(of)d(parallel)g(ine\016ciency:)62 2121 y
Fk(\017)21 b Fl(Synchr)n(onization)15 b(Overhe)n(ad)p
Fn(:)i(The)d(searc)o(h)g(t)o(ypically)d(has)i(man)o(y)e(sync)o
(hronization)i(p)q(oin)o(ts)f(that)h(result)h(in)e(a)h(high)104
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dup 0 exch lineto
exch dup 3 1 roll exch lineto
0 lineto
closepath
bgred bggreen bgblue setrgbcolor
eofill
SSten
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/Rast {
exch dup 3 1 roll 1 0 0 -1 0 6 -1 roll matrix astore
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/arrowhead {
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transform originalCTM itransform
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gsave
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newpath
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arrowHeight neg arrowWidth 2 div neg lineto
patternNone not {
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/padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul
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arrowHeight padtip add padtail add arrowHeight div dup scale
arrowheadpath
ifill
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brushNone not {
originalCTM setmatrix
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arrowheadpath
istroke
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grestore
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/arrowheadpath {
newpath
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arrowHeight neg arrowWidth 2 div neg lineto
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/leftarrow {
0 begin
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x exch get /tailx exch def
y exch get /tipy exch def
x exch get /tipx exch def
brushLeftArrow { tipx tipy tailx taily arrowhead } if
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x exch get /tailx exch def
brushRightArrow { tipx tipy tailx taily arrowhead } if
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} dup 0 4 dict put def
%I Idraw 10 Grid 6 6
Begin
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%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
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%I t
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%I
[
(if \(flag == UBOUND\) { beta = min\(beta,h_score\); })
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 96 693 ] concat
%I
[
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 483 ] concat
%I
[
(score = -INFINITY;)
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Begin %I Text
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0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 471 ] concat
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[
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 441 ] concat
%I
[
(/* Loop through moves in move list */)
] Text
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 429 ] concat
%I
[
(for\(i=1; \(i <= width && score <= beta\); i++ \) {)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 96 405 ] concat
%I
[
(make_move\(p, move[i]\);)
] Text
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Begin %I Text
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%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
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%I t
[ 1 0 0 1 96 387 ] concat
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[
(value = -PVS\(p, -upper, -lower, depth+1, plytogo-1\);)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
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%I t
[ 1 0 0 1 96 375 ] concat
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[
(if \(value > score && i > 1\) {)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 120 363 ] concat
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[
(value = -PVS\(p, -beta, -value, depth+1, plytogo-1\);)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 96 351 ] concat
%I
[
(})
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 96 333 ] concat
%I
[
(unmake_move\(p,move[i]\);)
] Text
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 96 309 ] concat
%I
[
(if \(value > score\) {)
] Text
End
Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 120 297 ] concat
%I
[
(score = value;)
] Text
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 120 285 ] concat
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[
(move_opt = move[i];)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 96 273 ] concat
%I
[
(})
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 96 255 ] concat
%I
[
(/* Set bounds for next search */)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 96 243 ] concat
%I
[
(lower = max\(alpha, score\); upper = lower+1;)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 231 ] concat
%I
[
(} /* for all moves */)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 195 ] concat
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[
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Begin %I Text
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0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 171 ] concat
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[
(h_flag = VALID;)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 561 ] concat
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[
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 159 ] concat
%I
[
(if \(score <= alpha\) { h_flag = UBOUND; })
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 147 ] concat
%I
[
(if \(score >= beta\) { h_flag = LBOUND; })
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 135 ] concat
%I
[
(if \(h_length <= plytogo\) {)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 96 123 ] concat
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[
(store\(p_hash, p_key, plytogo, score, h_flag, move_opt\);)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 111 ] concat
%I
[
(})
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 99 ] concat
%I
[
(return\(score\);)
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Begin %I Text
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%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 48 87 ] concat
%I
[
(} /* function PVS */)
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Begin %I Rect
%I b 65535
1 0 0 [] 0 SetB
%I cfg Black
0 0 0 SetCFg
%I cbg White
1 1 1 SetCBg
none SetP %I p n
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[ 2 -0 -0 2 -190 -34 ] concat
%I
107 47 323 503 Rect
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 627 ] concat
%I
[
(if \(plytogo <= 0\) { return\(evaluate\(p\)\); })
] Text
End
Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 717 ] concat
%I
[
(if \(aphid_master\(\) == FALSE && h_length == plytogo\) {)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 615 ] concat
%I
[
(if \(aphid_horizon\(depth\)\) {)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 537 ] concat
%I
[
(if \(aphid_checkalarm\(\) != FALSE\) {)
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End
Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 459 ] concat
%I
[
(aphid_intnode_start\(depth, p_hash, p_key\);)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 96 417 ] concat
%I
[
(aphid_intnode_move\(depth, &\(move[i]\)\);)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 96 321 ] concat
%I
[
(aphid_intnode_update\(depth, value\);)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 213 ] concat
%I
[
(if \(score >= beta\) { aphid_intnode_fixbound\(depth\); })
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 72 183 ] concat
%I
[
(aphid_intnode_end\(depth, &score\);)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 96 525 ] concat
%I
[
(terminate_search = TRUE;)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 96 603 ] concat
%I
[
(return\(aphid_eval_leaf\(alpha,beta,depth,p_hash,p_key\)\);)
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
Courier 10 SetF
%I t
[ 1 0 0 1 96 513 ] concat
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[
(return\(0\); /* Should exit PVS quickly when alarm on */)
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End %I eop
showpage
end
%%EndDocument
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390 2520 a Fn(Figure)14 b(3:)j(Ho)o(w)d(APHID)g(Mo)q(di\014es)g(A)g(T)
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%I b u
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[ 0.799705 0 0 0.799705 0 0 ] concat
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none SetB %I b n
%I cfg Black
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%I cbg White
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[ 1 -0 -0 1 -125 612 ] concat
%I
155 342 563 354 Rect
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Begin %I Text
%I cfg Black
0 0 0 SetCFg
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%I t
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%I b 65535
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[
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translate
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originalCTM setmatrix
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brushDashOffset -1 eq {
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brushDashArray brushDashOffset setdash
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originalCTM setmatrix
stroke
grestore
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gsave
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bgred bggreen bgblue setrgbcolor
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SSten
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transform originalCTM itransform
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transform originalCTM itransform
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originalCTM setmatrix
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%I t
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%I t
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[
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%I t
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[
(oldscore = -aphid_rootsearch\(depth+1,plytogo-1,-beta,-lower\);)
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[
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[
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%I t
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[
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Begin %I Text
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Begin %I Text
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[
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[
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%I t
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[
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Begin %I Text
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%I t
[ 1 0 0 1 84 653 ] concat
%I
[
(aphid_intnode_premove\(depth,&move[i]\);)
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Begin %I Text
%I cfg Black
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%I t
[ 1 0 0 1 84 593 ] concat
%I
[
(unmake_move\(p,move[i]\);)
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Begin %I Text
%I cfg Black
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%I t
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[
(-oldscore-delta-1, -oldscore-delta\);)
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Begin %I Text
%I cfg Black
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%I t
[ 1 0 0 1 84 617 ] concat
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[
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[
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[
(/* set new best move and score and research \(if necc.\) */)
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%I t
[ 1 0 0 1 60 665 ] concat
%I
[
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0 0 0 SetCFg
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%I t
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[
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Begin %I Text
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0 0 0 SetCFg
%I f -*-courier-medium-r-normal-*-10-*-*-*-*-*-*-*
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%I t
[ 1 0 0 1 60 563 ] concat
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[
(if \(newscore > oldscore+delta\) {)
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showpage
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%%EndDocument
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503 2661 a Fn(Figure)i(6:)k(Ho)o(w)13 b(APHID)h(Mo)q(di\014es)h(The)f
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b(ar)n(chite)n(ctur)n(e)25 b(lo)n(giciel)r(le)f(synth)o(\022)-20
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17 16 bop 0 195 a Fo(A)69 b(Description)21 b(of)i(APHID)f(In)n(terface)
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404 y(hierarc)o(h)o(y)m(,)13 b(whic)o(h)h(o)q(ccupies)h(the)f(highest)h
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476 y Fk(\017)21 b Fe(slave)p Fn(:)g(An)o(y)16 b(pro)q(cess)i(that)e(m)
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b(With)104 518 y(this)14 b(de\014nition,)f(a)g(pro)q(cess)j(is)e
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(not)g(b)q(e)g(b)q(oth.)62 589 y Fk(\017)21 b Fe(master)p
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(p)q(ossible)g(for)f(a)104 631 y(pro)q(cess)h(to)f(b)q(e)h(b)q(oth)f(a)
f(master)h(and)f(a)h(sla)o(v)o(e)g(if)f(the)h(pro)q(cess)i(hierarc)o(h)
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932 y Fk(\017)21 b Fe(APHID)p 217 932 14 2 v 14 w(HASHTYPESIZE)p
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1045 y(same)h(hash)h(v)n(alue)f(are)h(the)h(same.)62
1117 y Fk(\017)21 b Fe(APHID)p 217 1117 V 14 w(MOVESIZE)p
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1189 y Fk(\017)21 b Fe(APHID)p 217 1189 V 14 w(MINUSINF)15
b Fn(and)h Fe(APHID)p 615 1189 V 15 w(PLUSINF)p Fn(:)e(Sp)q
(eci\014cations)j(of)e(v)n(alues)h(smaller)f(than)h(the)h(minim)n(um)o
(,)c(and)j(larger)104 1230 y(than)e(the)g(maxim)n(um)o(,)c(that)k(the)h
(\\ev)n(aluation")d(could)i(p)q(ossibly)f(return,)i(resp)q(ectiv)o(ely)
m(.)62 1302 y Fk(\017)21 b Fe(APHID)p 217 1302 V 14 w(INVALIDSCORE)p
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(ted)h(b)o(y)e(the)h(minim)n(um)11 b(and)16 b(maxim)n(um)104
1344 y(v)n(alues)d(sp)q(eci\014ed)j(previously)m(.)62
1415 y Fk(\017)21 b Fe(APHID)p 217 1415 V 14 w(LOG2)p
319 1415 V 15 w(TABSIZE)p Fn(:)16 b(The)j(size)g(of)e(the)i(APHID)f
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(w)o(een)g(the)104 1457 y(master)c(and)h(the)g(sla)o(v)o(es,)g(tak)o
(en)f(to)h(a)f(base)i(2)e(logarithm.)21 b(F)m(or)15 b(example,)g(a)g(v)
n(alue)g(of)g(14)g(indicates)h(an)g(APHID)104 1503 y(table)e(with)f(2)
323 1488 y Fi(14)370 1503 y Fn(=)e(16384)i(en)o(tries.)62
1575 y Fk(\017)21 b Fe(APHID)p 217 1575 V 14 w(MAXSLAVEPLYSEARCH)p
Fn(:)7 b(The)j(maxim)o(um)c("plytogo")i(v)n(alue)i(that)g(y)o(ou)g
(could)g(p)q(ossibly)g(exp)q(ect)i(to)e(hand)g(to)g(a)104
1616 y(sla)o(v)o(e)g(to)g(searc)o(h.)18 b(Note)10 b(that)g(this)h(v)n
(alue)e(should)h(not)g(b)q(e)h(excessiv)o(ely)g(large,)g(since)g(this)f
(and)g Fe(APHID)p 1683 1616 V 15 w(LOG2)p 1786 1616 V
14 w(TABSIZE)104 1658 y Fn(are)k(the)h(leading)e(determinan)o(ts)g(in)h
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1802 y Fk(\017)21 b Fe(APHID)p 217 1802 V 14 w(SLAVENODESTOCOMM)p
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1843 y(visits)13 b(on)h(the)h(t)o(yp)q(e)f(of)f(pro)q(cessor)j(b)q
(eing)e(used,)g(divided)g(b)o(y)f(10.)0 1958 y Fc(A.3)56
b(Standard)19 b(V)-5 b(ariables)19 b(Used)62 2026 y Fk(\017)i
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(as)g(the)g(initial)104 2068 y(program.)62 2140 y Fk(\017)21
b Fe(depth)p Fn(:)c(The)d(n)o(um)o(b)q(er)f(of)g(ply)h(the)g(curren)o
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(game)d(tree.)62 2212 y Fk(\017)21 b Fe(plytogo)p Fn(:)15
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h(b)q(ottom)d(of)h(the)i(game)d(tree.)18 b(In)11 b(a)g(searc)o(h)h
(with)e(no)h(extensions)104 2253 y(or)j(forw)o(ard)f(pruning,)g
Fe(plytogo)21 b(+)g(depth)13 b Fn(should)h(b)q(e)g(constan)o(t.)62
2325 y Fk(\017)21 b Fe(&move[i])10 b Fn(or)i Fe(&bestmove)p
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1098 2325 V 15 w(MOVESIZE)f Fn(b)o(ytes)i(whic)o(h)g(sp)q(eci\014es)h
(the)g(mo)o(v)o(e)d(b)q(eing)104 2367 y(pla)o(y)o(ed.)62
2438 y Fk(\017)21 b Fe(p)p 129 2438 V 15 w(hash)p Fn(:)c(A)d(p)q(oin)o
(ter)g(to)g(an)g(area)g(of)f Fe(APHID)p 805 2438 V 15
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(hash)g(v)n(alue.)62 2510 y Fk(\017)21 b Fe(p)p 129 2510
V 15 w(key)p Fn(:)c(A)c(p)q(oin)o(ter)g(to)f(an)g(area)h
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(tains)h(a)f(lo)q(c)o(k)g(whic)o(h)h(can)g(\\guaran)o(tee")f(the)104
2552 y(b)q(oard)i(stored)h(in)e(the)h(lo)q(cation)f(of)h(the)g(hash)g
(table)g(is)g(correct.)62 2624 y Fk(\017)21 b Fe(alpha)13
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18 17 bop 0 195 a Fc(A.4)56 b(Stubs)19 b(T)-5 b(o)19
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304 263 14 2 v 15 w(stub)p 407 263 V 14 w(encodeinit\(char)e(*msg\))p
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(yte)g(bu\013er)i(to)104 305 y(store)g(all)d(p)q(ertinen)o(t)k
(information)14 b(ab)q(out)i(the)i(ro)q(ot)f(of)f(the)i(game)d(tree.)29
b(The)17 b(return)i(v)n(alue)d(is)h(the)g(n)o(um)o(b)q(er)g(of)104
346 y(b)o(ytes)d(used)h(in)f(the)g(string)g Fe(msg)p
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421 V 15 w(ln,)j(char)f(*msg\))p Fn(:)15 b(All)9 b(other)i(pro)q
(cesses)j(in)c(the)h(system,)f(aside)h(from)104 463 y(the)i(absolute)f
(master,)g(receiv)o(e)i(the)f(message)f(length)g(and)g(the)h(message)f
(enco)q(ded)i(b)o(y)e Fe(aphid)p 1606 463 V 15 w(stub)p
1709 463 V 15 w(encodeinit)p Fn(,)104 504 y(and)h(should)h(set)h(the)f
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428 579 V 15 w(movedownpath\(int)e(num)p 880 579 V 15
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(sla)o(v)o(es,)f(a)g(series)i(of)104 620 y Fe(num)p 173
620 V 15 w(moves)d Fn(mo)o(v)o(es)h(is)g(giv)o(en)h(in)f
Fe(movepath)p Fn(,)f(with)h(eac)o(h)h(mo)o(v)o(e)e(b)q(eing)i
Fe(APHID)p 1328 620 V 15 w(MOVESIZE)e Fn(b)o(ytes)i(long.)17
b(The)12 b(routine)104 662 y(should)h(pla)o(y)g(through)h(the)h(mo)o(v)
o(es)d(giv)o(en)i(in)f Fe(movepath)f Fn(from)h(the)h(ro)q(ot)g(of)f
(the)i(game)d(tree.)62 737 y Fk(\017)21 b Fe(void)g(aphid)p
326 737 V 14 w(stub)p 428 737 V 15 w(moveuppath\(int)e(num)p
836 737 V 15 w(moves,)i(char)g(*movepath\))p Fn(:)14
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778 y(pletely)j(undo)f(an)o(y)h(c)o(hanges)g(made)f(b)o(y)h
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15 w(stub)p 407 853 V 14 w(iterativedeepening\(i)o(nt)e(depth,)h(int)h
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(this)104 894 y(routine)j(should)f(return)i(the)g(searc)o(h)g(depth)f
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(master's)g(tree.)28 b(F)m(or)104 936 y(most)12 b(programs)h(that)h(do)
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428 1011 V 15 w(preparesearch\(int)e(depth,)h(int)h(plytogo,)f(int)i
(winstats[],)d(int)i(*alpha,)104 1052 y(int)g(*beta\))p
Fn(:)16 b(Called)10 b(b)o(y)i(the)g(sla)o(v)o(es,)f(this)h(routine)g
(sets)g(the)g(initial)e(windo)o(w)h(searc)o(hed)i(b)o(y)e(the)h(sla)o
(v)o(es.)17 b(Statistics)104 1094 y(on)12 b(previous)h(searc)o(hes)h
(and)f(the)g(curren)o(t)h(guessed)g(score)g(at)e(the)h(ro)q(ot)g(are)f
(passed)i(in)e(via)g(the)h Fe(winstats[])d Fn(arra)o(y)m(.)104
1135 y(The)j(routine)f(should)h(set)g Fe(*alpha)e Fn(and)h
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g(states)j(ha)o(v)o(e)e(b)q(een)i(turned)g(o\013.)62
1251 y Fk(\017)21 b Fe(int)g(aphid)p 304 1251 V 15 w(stub)p
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(should)g(call)g(y)o(our)g(implem)o(en)o(tation)d(of)j
Fm(\013\014)r Fn(,)g(and)g(return)h(the)g(minim)o(ax)104
1334 y(v)n(alue)g(bac)o(k)h(to)g(the)g(APHID)g(library)m(.)62
1409 y Fk(\017)21 b Fe(int)g(aphid)p 304 1409 V 15 w(stub)p
407 1409 V 14 w(evaluate\(int)f(depth,)g(int)i(alpha,)e(int)h(beta\))p
Fn(:)c(Called)c(b)o(y)g(the)h(master)f(the)h(\014rst)g(time)104
1451 y(it)g(visits)h(a)f(leaf)g(of)g(its)h(tree,)g(this)g(routine)g
(should)f(simply)f(call)h(y)o(our)g(ev)n(aluation)f(routine)i(and)g
(return)g(the)h(score)104 1492 y(for)d(the)i(p)q(osition)e(reac)o(hed)i
(at)f Fe(depth)f Fn(ply)g(within)g(the)i(tree.)62 1567
y Fk(\017)21 b Fe(int)g(aphid)p 304 1567 V 15 w(stub)p
407 1567 V 14 w(stopsearch\(int)e(pass)p 836 1567 V 15
w(stats[]\))p Fn(:)j(Called)16 b(only)f(b)o(y)i(the)g(absolute)f
(master)g(pro)q(cess,)j(this)104 1608 y(routine)d(should)g(c)o(hec)o(k)
h(y)o(our)e(timer)g(and)h(determine)g(if)f(y)o(our)h(time)e(limit)f
(has)k(b)q(een)g(exceeded)h(for)d(a)h(searc)o(h.)25 b(If)104
1650 y(the)14 b(time)f(limit)e(has)j(b)q(een)h(exceeded,)h(this)e
(routine)g(should)f(return)i(1;)f(otherwise,)g(0.)62
1725 y Fk(\017)21 b Fe(int)g(aphid)p 304 1725 V 15 w(stub)p
407 1725 V 14 w(visited\(\))p Fn(:)c(Called)d(b)o(y)g(the)g(sla)o(v)o
(es,)g(this)g(should)g(return)i(a)e(global)e(coun)o(t)j(of)e(the)i(n)o
(um)o(b)q(er)f(of)104 1766 y(no)q(des)g(visited)g(b)o(y)g(the)g
(program.)0 1882 y Fc(A.5)56 b(In)n(terface)18 b(Calls)h(Used)f(b)n(y)h
(Master)g(and)g(Sla)n(v)n(e)62 1951 y Fk(\017)i Fe(void)g(aphid)p
326 1951 V 14 w(startup\(argv\))p Fn(:)k(In)19 b(the)g(\014rst)h(pro)q
(cess)g(run,)g(PVM)f(is)g(spa)o(wned)g(on)g(the)g(mac)o(hines)f(sp)q
(eci\014ed,)104 1992 y(and)c(a)f(sla)o(v)o(e)h(pro)q(cess)i(is)e(spa)o
(wned)g(with)g(the)h(same)e(argumen)o(t)g(list)g Fe(\(argv\))g
Fn(as)h(the)h(master,)e(as)h(sp)q(eci\014ed)i(b)o(y)d(the)104
2034 y Fe(aphid.config)e Fn(\014le.)18 b(In)c(a)g(spa)o(wned)g(pro)q
(cess,)h(the)g(APHID)f(library)f(nev)o(er)i(exits)f(this)g(function)g
(call.)62 2108 y Fk(\017)21 b Fe(void)g(aphid)p 326 2108
V 14 w(exit\(\))p Fn(:)j(This)17 b(routine)h(remo)o(v)o(es)e(a)h(pro)q
(cess)j(from)15 b(the)j(PVM)g(group,)f(and)g(it)g(should)g(b)q(e)h
(called)104 2150 y(b)q(efore)e(an)o(y)f(pro)q(cess)j(exits)e(\(due)g
(to)g(errors)h(or)e(normal)f(completion\).)21 b(If)16
b(the)g(pro)q(cess)h(is)f(the)g(absolute)g(master,)104
2191 y(completion)11 b(of)i(this)h(routine)f(ensures)j(that)d(all)f(of)
h(the)h(spa)o(wned)g(pro)q(cesses)i(ha)o(v)o(e)d(b)q(een)i(sh)o(ut)f
(do)o(wn)f(successfully)m(.)62 2266 y Fk(\017)21 b Fe(int)g(aphid)p
304 2266 V 15 w(master\(\))p Fn(:)16 b(Returns)f(1)e(if)g(the)i(pro)q
(cess)h(is)d(a)h(master)f(in)h(the)g(hierarc)o(h)o(y)m(,)g(and)f(0)h
(otherwise.)62 2341 y Fk(\017)21 b Fe(int)g(aphid)p 304
2341 V 15 w(slave\(\))p Fn(:)14 b(Returns)d(1)f(if)g(the)h(pro)q(cess)h
(w)o(as)e(spa)o(wned,)h(returns)h(0)e(if)f(it)h(is)g(the)h(absolute)f
(master)g(pro)q(cess)104 2382 y(whic)o(h)k(spa)o(wned)h(the)g(other)g
(pro)q(cesses.)23 b(Note)15 b(that)f(a)h(pro)q(cess)h(can)f(b)q(e)g(b)q
(oth)f(a)h(sla)o(v)o(e)f(and)g(a)g(master)g(dep)q(ending)104
2424 y(on)f(the)i(hierarc)o(h)o(y)f(sp)q(eci\014ed)i(in)d
Fe(aphid.config)p Fn(.)954 2828 y(18)p eop
%%Page: 19 19
19 18 bop 0 195 a Fc(A.6)56 b(In)n(terface)18 b(Calls)h(Used)f(b)n(y)h
(Masters)g(Only)62 263 y Fk(\017)i Fe(void)g(aphid)p
326 263 14 2 v 14 w(initserach\(int)e(maxdepth\))p Fn(:)d(Called)d(b)o
(y)h(the)g(absolute)g(master)g(pro)q(cess,)h(this)f(pro)q(cedure)h
(pre-)104 305 y(pares)i(to)g(start)g(a)f(searc)o(h)i(in)e(parallel.)26
b(This)16 b(routine)h(calls)f Fe(aphid)p 1212 305 V 15
w(stub)p 1315 305 V 15 w(encodeinit)p Fn(,)f(and)h(then)h(informs)e
(all)104 346 y(of)e(the)i(other)g(pro)q(cesses)i(of)c(the)i(curren)o(t)
h(state)f(of)e(the)i(game.)i(The)e(parameter)f(indicates)g(the)h(maxim)
n(um)10 b(depth)104 388 y(that)k(an)o(y)f(pro)q(cess)j(is)e(nominall)o
(y)d(allo)o(w)o(ed)i(to)g(searc)o(h,)i Fl(not)g(including)h(se)n(ar)n
(ch)e(extensions)p Fn(.)62 463 y Fk(\017)21 b Fe(int)g(aphid)p
304 463 V 15 w(rootsearch\(int)e(depth,)h(int)h(plytogo,)f(int)i
(alpha,)e(int)h(beta\))p Fn(:)26 b(This)18 b(routine)h(is)f(called)104
504 y(b)o(y)d(the)h(absolute)g(master,)e(instead)i(of)f(calling)f(the)i
(t)o(ypical)f Fm(\013\014)i Fn(implemen)o(taiton.)i(It)d(allo)o(ws)e(a)
h(master)g(pro)q(cess)104 546 y(to)i(do)g(m)o(ultiple)e(passes)k(of)e
(the)h(tree)g(un)o(til)f(the)h(searc)o(h)g(is)g(completed,)f(or)g(the)h
(alarm)d(has)j(b)q(een)g(signalled)f(via)104 587 y Fe(aphid)p
217 587 V 14 w(stub)p 319 587 V 15 w(stopsearch)p Fn(.)f(If)e(the)g
(searc)o(h)i(is)d(allo)o(w)o(ed)g(to)h(complete,)f(this)h(routine)g
(returns)h(the)g(minim)o(ax)c(v)n(alue)104 629 y(of)i(the)i(tree)g
(that)f(it)f(has)h(b)q(een)h(ask)o(ed)f(to)g(searc)o(h.)62
703 y Fk(\017)21 b Fe(int)g(aphid)p 304 703 V 15 w(intnode)p
473 703 V 14 w(premove\(int)e(depth,)i(char)g(*moveptr\))p
Fn(:)15 b(Called)d(b)o(y)h(the)g(absolute)g(master,)e(this)i(rou-)104
745 y(tine)h(stores)h(mo)o(v)o(es)e(made)f(b)q(efore)j(a)f(call)f(to)g
Fe(aphid)p 938 745 V 15 w(rootsearch)f Fn(in)h(the)i(mo)o(v)o(e)d
(list.)62 820 y Fk(\017)21 b Fe(void)g(aphid)p 326 820
V 14 w(endsearch\(\))p Fn(:)15 b(The)e(absolute)f(master)g(should)g
(call)f(this)i(routine)f(when)h(it)f(is)g(\014nished)h(searc)o(hing)f
(a)104 861 y(tree)i(that)e(has)h(b)q(een)h(called)e(;)h(it)f(stops)h
(the)g(sla)o(v)o(es)g(from)e(w)o(orking)g(on)i(the)g(lea)o(v)o(es)g(of)
f(the)h(game)e(tree)j(and)e(prepares)104 903 y(the)i(sla)o(v)o(es)g(to)
g(receiv)o(e)h(a)f(new)g(ro)q(ot)g(p)q(osition.)62 977
y Fk(\017)21 b Fe(void)g(aphid)p 326 977 V 14 w(horizon\(int)f(depth\))
p Fn(:)15 b(A)d(\\master")e(pro)q(cess)j(calls)e(this)h(routine)f(to)g
(determine)h(if)e(it)h(has)h(reac)o(hed)104 1019 y(its)i(arti\014cial)f
(horizon.)62 1094 y Fk(\017)21 b Fe(void)g(aphid)p 326
1094 V 14 w(eval)p 428 1094 V 15 w(leaf\(int)f(alpha,)h(int)g(beta,)g
(int)g(depth,)g(char)g(*p)p 1403 1094 V 15 w(hash,)g(char)g(*p)p
1702 1094 V 15 w(key\))p Fn(:)104 1135 y(This)10 b(routine)h
(determines)g(a)f(score)i(v)n(alue)d(for)h(the)i(leaf,)e(based)h(on)f
(the)h(b)q(est)h(information)7 b(a)o(v)n(ailable)h(to)j(the)g(master.)
104 1177 y Fe(p)p 129 1177 V 15 w(hash)i Fn(and)h Fe(p)p
348 1177 V 15 w(key)g Fn(are)g(required)h(to)f(determine)f(if)g(this)h
(no)q(de)h(has)f(b)q(een)h(previously)e(visited.)62 1251
y Fk(\017)21 b Fe(void)g(aphid)p 326 1251 V 14 w(intnode)p
494 1251 V 15 w(start\(int)f(depth,)g(char)h(*p)p 1032
1251 V 15 w(hash,)g(char)g(*p)p 1331 1251 V 15 w(key\))p
Fn(:)16 b(Called)11 b(b)o(y)g(a)h(master)f(pro)q(cess,)104
1293 y(this)j(routine)g(initializes)e(b)q(ound)i(gathering)g
(information)d(for)i(an)h(in)o(terior)f(no)q(de)h(within)f(the)i(game)d
(tree.)19 b Fe(p)p 1850 1293 V 16 w(hash)104 1334 y Fn(and)13
b Fe(p)p 209 1334 V 16 w(key)g Fn(are)h(required)h(to)f(determine)g(if)
f(this)h(no)q(de)g(has)g(b)q(een)h(previously)f(visited.)62
1409 y Fk(\017)21 b Fe(void)g(aphid)p 326 1409 V 14 w(intnode)p
494 1409 V 15 w(move\(int)f(depth,)g(char)h(*moveptr\))p
Fn(:)k(Called)18 b(b)o(y)g(a)g(master)g(pro)q(cess,)i(this)f(routine)
104 1451 y(inserts)c(the)f(mo)o(v)o(e)e(p)q(oin)o(ted)i(to)f(b)o(y)h
Fe(moveptr)e Fn(in)o(to)h(a)h(hidden)g(mo)o(v)o(e)e(list)h(that)h(will)
e(ev)o(en)o(tually)h(b)q(e)i(sen)o(t)f(to)g(a)f(sla)o(v)o(e)104
1492 y(in)g Fe(aphid)p 265 1492 V 15 w(eval)p 368 1492
V 15 w(leaf)p Fn(.)62 1567 y Fk(\017)21 b Fe(void)g(aphid)p
326 1567 V 14 w(intnode)p 494 1567 V 15 w(update\(int)e(depth,)i(int)g
(value\))p Fn(:)27 b(Called)19 b(b)o(y)f(the)i(master)f(pro)q(cess,)j
(this)d(routine)104 1608 y(tak)o(es)d(the)g(v)n(alue)f(returned)j(b)o
(y)d(the)i(c)o(hild)e Fm(\013\014)j Fn(call)d(and)h(uses)h(it)e(to)h
(up)q(date)g(the)h(hidden)e(\\b)q(ound")h(information)104
1650 y(gathered)f(for)e(ev)o(ery)i(no)q(de)f(in)f(the)i(master's)e
(tree.)62 1725 y Fk(\017)21 b Fe(void)g(aphid)p 326 1725
V 14 w(intnode)p 494 1725 V 15 w(fixbound\(int)e(depth\))p
Fn(:)h(In)c(the)g(case)h(of)e(a)h(cuto\013,)g(this)g(routine)g(will)e
(\014x)h(the)i(hidden)104 1766 y(b)q(ound)d(information)d(when)j(not)g
(all)f(mo)o(v)o(es)f(ha)o(v)o(e)i(b)q(een)h(fully)d(explored.)62
1841 y Fk(\017)21 b Fe(void)g(aphid)p 326 1841 V 14 w(intnode)p
494 1841 V 15 w(end\(int)f(depth,)h(int)g(*score\))p
Fn(;)12 b(This)j(routine)f(is)g(called)g(b)o(y)h(a)f(master)f(for)h(ev)
o(ery)i(in-)104 1882 y(ternal)d(no)q(de)g(within)f(the)i(tree,)g(and)e
(ensures)j(that)e(the)g(score)i(returned)f(is)f(consisten)o(t)h(with)e
(previously)h(gathered)104 1924 y(information)e(ab)q(out)j(the)g(no)q
(de.)0 2040 y Fc(A.7)56 b(In)n(terface)18 b(Calls)h(Used)f(b)n(y)h(Sla)
n(v)n(es)g(Only)62 2108 y Fk(\017)i Fe(int)g(aphid)p
304 2108 V 15 w(checkalarm\(\))p Fn(:)e(This)d(routine)h(c)o(hec)o(ks)g
(to)f(see)h(if)f(a)f(searc)o(h)j(should)e(b)q(e)g(terminated.)24
b(If)16 b(the)h(v)n(alue)104 2150 y(returned)f(is)e(equal)f(to)h(0,)g
(the)h(searc)o(h)g(should)f(con)o(tin)o(ue.)19 b(If)13
b(the)i(v)n(alue)f(returned)h(is)f(not)h(equal)e(to)h(0,)g(the)g
(curren)o(t)104 2191 y(searc)o(h)h(has)f(b)q(een)h(in)o(terrupted,)g
(and)e(w)o(e)h(should)g(terminate)f(it)h(in)f(a)h(\\nice")g(w)o(a)o(y)m
(.)954 2828 y(19)p eop
%%Page: 20 20
20 19 bop 0 195 a Fc(A.8)56 b(The)18 b(\\aphid.con\014g")h(File)e
(Description)62 263 y Fk(\017)k Fn(The)15 b(\014rst)g(line)f(con)o
(tains)h(t)o(w)o(o)f(in)o(tegers:)21 b(The)15 b(n)o(um)o(b)q(er)f(of)g
(lev)o(els)g(in)g(the)i(pro)q(cess)g(hierarc)o(h)o(y)m(,)e(and)h(the)g
(minim)n(um)104 305 y(gran)o(ularit)o(y)d(of)i(w)o(ork)f(that)h(w)o(e)g
(are)h(allo)q(cated)e(in)g(parallel.)62 380 y Fk(\017)21
b Fn(The)d(next)g(lines)g(eac)o(h)g(con)o(tain)g(one)g(in)o(teger,)g
(eac)o(h)g(in)o(teger)h(represen)o(ting)g(the)f(v)n(alue)g(of)f
Fm(d)1607 365 y Fd(0)1636 380 y Fn(for)g(a)h(lev)o(el)f(in)g(the)104
421 y(pro)q(cess)e(hierarc)o(h)o(y)m(.)62 496 y Fk(\017)21
b Fn(The)14 b(last)g(lines)g(indicate)h(what)f(mac)o(hines)f(the)i(pro)
q(cesses)i(should)c(b)q(e)i(spa)o(wned)g(on,)f(and)g(what)g(executable)
h(is)f(to)104 537 y(b)q(e)j(run,)g(one)g(line)f(p)q(er)i(pro)q(cess)g
(to)f(b)q(e)g(spa)o(wned.)27 b(By)17 b(default,)f(APHID)h(will)e(spa)o
(wn)i(an)f(executable)i(with)e(the)104 579 y(same)d(program)f(name)h
(as)h(the)h(original)d(program)g(unless)j(a)f Fe(#)f
Fn(c)o(haracter)j(app)q(ears)e(on)g(the)h(line,)e(whic)o(h)h(indicates)
104 620 y(a)h(separation)h(b)q(et)o(w)o(een)h(the)f(mac)o(hine)e(name)g
(and)i(the)g(program)e(name.)22 b(The)16 b(absolute)f(master)g(pro)q
(cess)j(is)d(not)104 662 y(listed)c(in)f(this)h(hierarc)o(h)o(y)m(.)17
b(A)10 b(pro)q(cess)j(hierarc)o(h)o(y)e(can)g(b)q(e)g(sp)q(eci\014ed)i
(using)d(tabs)h(to)g(mo)o(v)o(e)e(the)i(start)h(of)e(the)h(mac)o(hine)
104 703 y(name)h(o)o(v)o(er)i(in)g(the)g(\014le.)954
2828 y(20)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF
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