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63 % author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry",
65 % date = "22 June 1996",
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67 % email = "kb@@mail.tug.org",
68 % address = "135 Center Hill Rd. // Plymouth, MA 02360",
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81 % positions, because some Windows users cannot easily reencode the
82 % fonts, and it makes no difference on other systems. The only Windows
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85 % (173). quotesingle and grave are moved just because it's such an
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926 50 b(The)32 b Fq(\013)q(\014)37 b Fu(algorithm)30 b([9])i(is)f(used)h
927 (to)f(e)o(xhausti)n(v)o(ely)0 1199 y(search)c(v)n(ariations)d(that)i
928 (are)g Fq(d)g Fu(mo)o(v)o(es)e(deep)i(in)g(a)g(depth-\002rst)g(manner)g
929 (to)g(determine)f(the)h(best)f(mo)o(v)o(e)g(and)h(its)0
930 1398 y(v)n(alue.)k(A)25 b(lar)n(ge)g(hash)g(table,)g(called)f(the)h
931 Fm(tr)o(ansposition)c(table)k Fu([5],)g(is)f(used)h(to)f(store)h(pre)n
932 (viously)e(determined)0 1598 y(best)31 b(mo)o(v)o(es)e(and)i(v)n(alues)
933 g(for)g(positions.)48 b(The)31 b(v)n(alues)f(from)h(this)f(table)h(are)
934 h(re-used)f(during)g(the)g(search)g(to)0 1797 y(pre)n(v)o(ent)24
935 b(the)g(same)h(position)e(from)i(being)f(e)o(xplored)g(twice.)146
936 1996 y(Instead)31 b(of)h(immediately)d(searching)i(a)h(v)n(ariation)e
937 Fq(d)h Fu(mo)o(v)o(es)e(deep)j(\(or)f Fq(d)g Fm(ply)p
938 Fu(\),)i(most)d(programs)h(search)0 2195 y(to)c(1)g(ply)-6
939 b(,)27 b(then)f(to)h(2)g(ply)-6 b(,)27 b Fm(et)g(ceter)o(a)p
940 Fu(.)38 b(This)26 b(technique)h(is)g(kno)n(wn)f(as)h
941 Fm(iter)o(ative)f(deepening)h Fu([16)o(],)h(and)g(is)e(used)0
942 2395 y(to)i(acquire)g(mo)o(v)o(e-ordering)f(information)f(in)i(the)g
943 (transposition)e(table.)41 b(The)28 b(best)g(mo)o(v)o(e)e(for)j(a)f
944 Fl(\()p Fq(d)d Fk(\000)g Fl(1\))p Fu(-ply)0 2594 y(search)30
945 b(is)f(lik)o(ely)f(to)h(be)g(the)g(best)g(mo)o(v)o(e)f(for)h(a)h
946 Fq(d)p Fu(-ply)e(search,)j(and)e(the)g Fq(\013)q(\014)35
947 b Fu(algorithm)28 b(will)g(b)n(uild)g(a)i(smaller)0 2793
948 y(search)25 b(tree)h(\(by)e(eliminating,)f(or)i(cutting-of)n(f,)e
949 (irrele)n(v)n(ant)h(subtrees\))h(if)f(the)h(best)f(mo)o(v)o(e)g(is)g
950 (searched)h(\002rst.)146 2992 y(A)f(game-playing)f(program)g(that)h
951 (can)g(out-search)g(its)f(opponent)g(has)g(a)i(high)e(probability)f(of)
952 i(winning.)29 b(It)0 3192 y(has)23 b(been)g(sho)n(wn)f(that)h(there)g
953 (is)g(a)g(strong)f(correlation)h(between)g(the)g(search)h(depth)e(and)h
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955 (check)o(ers)g(programs)f([8].)31 b(Thus,)24 b(programs)g(are)h(de)n(v)
956 o(eloped)e(to)i(search)g(as)g(deeply)f(as)0 3590 y(possible)f(while)i
957 (staying)e(within)h(the)h(time)f(constraints)f(imposed)h(by)g(the)h
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959 (search)i(game)e(trees)h(deeper)l(,)h(almost)d(all)i(of)f(the)h
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961 i(search)g(algorithms.)50 b(These)32 b(algorithms)e(force)j(w)o(ork)f
962 (on)f(one)h(part)g(of)g(the)g(tree)0 4188 y(to)c(be)g(completed)g
963 (before)g(w)o(ork)h(on)f(the)g(rest)g(of)g(the)g(tree)h(can)g(be)f
964 (carried)h(out.)40 b(There)29 b(are)g(global)e(synchro-)0
965 4387 y(nization)j(points)g(during)g(the)h(search)h(that)e(all)h
966 (processors)g(must)f(reach)i(before)f(an)o(y)g(process)g(is)f(allo)n
967 (wed)g(to)0 4586 y(proceed.)j(In)25 b(some)g(synchronous)f(algorithms,)
968 g(the)h(w)o(ork)g(is)g(synchronized)g(at)g(e)n(v)o(ery)g(choice)h
969 (along)e(the)i(hy-)0 4786 y(pothesized)i(best-mo)o(v)o(e)e(sequence,)k
970 (commonly)c(kno)n(wn)h(as)i(the)f(principal)g(v)n(ariation.)40
971 b(In)29 b(all)f(synchronized)0 4985 y(algorithms,)23
972 b(the)i(w)o(ork)f(is)h(synchronized)f(at)h(the)g(root)f(of)h(the)g
973 (tree)g(between)g(steps)f(of)h(iterati)n(v)o(e)f(deepening;)g(a)p
974 0 5074 1560 4 v 112 5136 a Fj(1)149 5166 y Fi(Othello)c(is)h(a)g(re)o
975 (gistered)e(trademark)f(of)i(Tsukuda)f(Original,)g(licensed)h(by)g
976 (Anjar)f(Co.)1925 5589 y Fu(1)p eop
978 2 4 bop 0 100 a Fu(complete)24 b Fq(d)p Fu(-ply)g(search)i(must)d(be)i
979 (\002nished)g(before)g(the)g Fl(\()p Fq(d)c Fl(+)h(1\))p
980 Fu(-ply)j(search)g(can)g(be)o(gin.)146 299 y(The)33 b(adv)n(antage)f
981 (of)h(the)f(synchronous)f(approaches)i(is)f(that)g(the)o(y)g(can)h(use)
982 f(the)h(v)n(alue)f(of)g(the)h(principal)0 498 y(v)n(ariation)19
983 b(in)h(the)h(same)f(w)o(ay)g(as)h(the)f(sequential)g(search)h
984 (algorithm)e(does.)29 b(Synchronous)19 b(parallel)i(algorithms)0
985 697 y(are)32 b(successful)e(at)h(k)o(eeping)f(the)h(size)f(of)h(the)g
986 (search)g(tree)h(b)n(uilt)d(close)i(to)f(the)h(sequential)f(search)h
987 (tree)g(size,)0 897 y(assuming)d(that)h(processors)g(are)i(able)e(to)g
988 (share)h(transposition)e(table)h(information)f(in)h(an)h(ef)n
989 (\002cient)g(manner)-5 b(.)0 1096 y(Ho)n(we)n(v)o(er)l(,)23
990 b(there)j(are)f(fundamental)f(problems)g(with)g(synchronous)f(parallel)
991 i Fq(\013)q(\014)30 b Fu(search)c(algorithms:)120 1347
992 y(1.)49 b(There)28 b(are)g(man)o(y)e(times)h(when)g(there)h(is)f(insuf)
993 n(\002cient)f(parallelism)g(to)h(k)o(eep)h(all)f(the)g(processors)g(b)n
994 (usy)-6 b(.)244 1546 y(If)29 b(there)f(are)i(more)e(processors)g(than)g
995 (w)o(ork)g(granules)h(at)f(a)h(synchronization)e(point,)h(then)g(some)g
996 (pro-)244 1746 y(cessors)23 b(must)g(go)g(idle.)30 b(This)23
997 b(idle)g(time)g(increases)h(in)f(magnitude)f(\(and)i(signi\002cance\))g
998 (as)f(the)h(number)244 1945 y(of)35 b(processors)f(increases.)61
999 b(This)35 b(problem)f(is)g(e)o(xacerbated)h(in)g(games)f(that)g(ha)n(v)
1000 o(e)h(a)g(small)f(a)n(v)o(erage)244 2144 y(number)24
1001 b(of)h(mo)o(v)o(e)e(choices.)120 2412 y(2.)49 b(The)o(y)33
1002 b(require)i(an)f(ef)n(\002cient)h(implementation)c(of)k(a)f(shared)h
1003 (transposition)d(table)i(between)g(the)g(pro-)244 2612
1004 y(cesses)24 b(to)f(achie)n(v)o(e)g(high)f(performance.)31
1005 b(T)-8 b(ypically)i(,)22 b(the)i(algorithms)e(will)g(e)o(xhibit)g(poor)
1006 i(performance)244 2811 y(without)19 b(such)i(a)g(table,)g(since)g(each)
1007 h(processor')-5 b(s)20 b(search)h(results)f(must)g(be)h(made)g(a)n(v)n
1008 (ailable)f(to)h(all)f(other)244 3010 y(processes.)37
1009 b(Because)28 b(of)f(this,)g(most)e(synchronous)h(algorithms)f(are)j
1010 (tested)f(on)f(shared)h(memory)g(sys-)244 3209 y(tems.)45
1011 b(On)29 b(distrib)n(uted)g(memory)f(systems,)i(sharing)f(a)h(table)g
1012 (is)f(not)g(as)h(ef)n(\002cient,)h(and)f(the)g(speedups)244
1013 3409 y(portrayed)25 b(in)f(the)h(literature)f(for)h(shared)g(memory)f
1014 (systems)g(are)h(not)f(achie)n(v)n(able.)120 3677 y(3.)49
1015 b(Man)o(y)25 b(synchronous)f(algorithms)g(attempt)h(to)g(initiate)g
1016 (parallelism)f(at)i(nodes)f(which)g(are)i(better)e(done)244
1017 3876 y(sequentially)-6 b(.)59 b(F)o(or)35 b(e)o(xample,)h(ha)n(ving)e
1018 (searched)h(the)g(\002rst)g(branch)g(at)g(a)g(node)g(and)g(not)f(achie)
1019 n(v)o(ed)g(a)244 4075 y(cut-of)n(f,)40 b(the)d(remaining)f(branches)i
1020 (are)g(usually)e(searched)h(in)g(parallel.)68 b(Ho)n(we)n(v)o(er)l(,)39
1021 b(if)e(the)g(second)244 4275 y(branch)26 b(causes)f(a)h(cut-of)n(f,)f
1022 (then)g(all)h(of)f(the)h(w)o(ork)f(done)g(on)g(the)h(third)f(and)g
1023 (subsequent)f(branches)i(w)o(as)244 4474 y(unnecessary)-6
1024 b(.)38 b(This)26 b(suggests)g(that)h(parallelism)f(should)g(only)h(be)g
1025 (initiated)f(at)h(nodes)g(where)h(there)g(is)244 4673
1026 y(a)d(high)f(probability)f(that)i(all)f(branches)h(must)f(be)h
1027 (considered.)120 4941 y(4.)49 b(Man)o(y)21 b(of)h(the)f(synchronous)g
1028 (algorithms)f(do)i(not)f(inte)o(grate)g(well)h(into)f(typical)g
1029 (sequential)g(algorithms.)244 5141 y(This)h(causes)h(man)o(y)f(changes)
1030 h(to)g(the)f(main)h(search)g(algorithm)f(to)g(incorporate)h
1031 (parallelism.)29 b(This)22 b(will)244 5340 y(lik)o(ely)i(result)g(in)g
1032 (a)i(parallel)e(program)h(for)g(which)f(it)g(is)h(dif)n(\002cult)f(to)g
1033 (v)o(erify)g(its)h(correctness.)1925 5589 y(2)p eop
1035 3 5 bop 146 100 a Fu(In)28 b(other)e(w)o(ork,)i(a)f(theoretical)g
1036 (model)f(w)o(as)h(de)n(v)o(eloped)f(for)i(comparing)e(a)h(typical)g
1037 (synchronous)f(game-)0 299 y(tree)31 b(search)g(algorithm)e(to)h(an)g
1038 (asynchronous)g(one)g([2].)48 b(The)30 b(theoretical)g(results)g
1039 (indicated)g(that)g(an)g(asyn-)0 498 y(chronous)22 b(algorithm)f(could)
1040 i(outperform)f(a)h(synchronous)f(algorithm)f(on)h(game)h(trees)g
1041 (similar)e(to)i(those)f(seen)0 697 y(in)j(practice.)34
1042 b(This)25 b(paper)h(sho)n(ws)f(that)g(it)g(is)g(possible)g(for)h
1043 (asynchronous)e(search)i(algorithms)e(to)i(outperform)0
1044 897 y(their)f(synchronous)e(counterparts)h(in)h(practice.)146
1045 1096 y(The)g(paper')-5 b(s)25 b(major)f(contrib)n(utions)f(include:)120
1046 1365 y(1.)49 b(The)36 b(APHID)g(\(Asynchronous)f(P)o(arallel)h
1047 (Hierarchical)h(Iterati)n(v)o(e)e(Deepening\))h(algorithm)e(is)i
1048 (intro-)244 1564 y(duced)19 b(that)f(addresses)h(the)f(pre)n(viously)f
1049 (mentioned)h(problems.)28 b(First,)19 b(the)g(algorithm)e(is)i
1050 (asynchronous)244 1764 y(in)k(nature;)h(it)f(remo)o(v)o(es)f(all)h
1051 (global)f(synchronization)g(points)h(from)g(the)g Fq(\013)q(\014)29
1052 b Fu(search)24 b(and)f(from)h(iterati)n(v)o(e)244 1963
1053 y(deepening.)62 b(Second,)38 b(the)d(algorithm)f(does)h(not)g(require)h
1054 (a)f(shared)h(transposition)d(table)i(for)h(mo)o(v)o(e)244
1055 2162 y(ordering)22 b(information.)28 b(Third,)23 b(parallelism)e(is)h
1056 (only)f(applied)h(at)g(nodes)g(that)g(ha)n(v)o(e)g(a)h(high)f
1057 (probability)244 2361 y(of)j(needing)f(parallelism.)120
1058 2634 y(2.)49 b(APHID)25 b(has)g(been)g(designed)f(to)g(conform)h(to)f
1059 (the)h(structure)f(of)h(the)g(sequential)f Fq(\013)q(\014)6
1060 b Fu(-based)24 b(game-tree)244 2833 y(search)35 b(algorithm.)57
1061 b(Consequently)-6 b(,)35 b(parallelism)e(can)i(be)f(added)g(to)g(an)g
1062 (e)o(xisting)f(application)g(with)244 3033 y(minimal)d(ef)n(fort.)50
1063 b(APHID)32 b(has)g(been)g(programmed)e(as)i(an)g
1064 (application-independent)d(and)j(portable)244 3232 y(library)-6
1065 b(.)529 3196 y Fn(2)624 3232 y Fu(This)33 b(w)o(as)g(used)g(to)g
1066 (generate)h(all)f(of)h(the)f(parallel)g(applications)f(reported)i(in)f
1067 (this)f(article.)244 3431 y(Each)25 b(of)g(the)g(implementations)e
1068 (took)h(less)h(than)g(a)g(day)g(of)h(programming)d(time)i(to)f(achie)n
1069 (v)o(e)h(a)g(parallel)244 3630 y(program)k(that)g(e)o(x)o(ecuted)f(in)h
1070 (the)h(same)f(w)o(ay)g(as)h(the)f(sequential)f(program,)i(and)g(a)f(fe)
1071 n(w)h(days)f(of)g(addi-)244 3830 y(tional)i(tuning)g(to)h(achie)n(v)o
1072 (e)g(the)g(reported)g(speedups.)53 b(In)32 b(contrast,)i(adding)e(a)g
1073 (synchronous)f(parallel)244 4029 y(algorithm)23 b(to)i(an)g(e)o
1074 (xisting)e(sequential)g(algorithm)h(may)g(tak)o(e)h(months)e(of)i(w)o
1075 (ork.)120 4302 y(3.)49 b(APHID')-5 b(s)31 b(performance)h(for)g(four)f
1076 (game-playing)f(programs)h(is)g(presented.)50 b(APHID)32
1077 b(yields)e(better)244 4501 y(speedups)38 b(than)h(synchronous)f(search)
1078 h(methods)f(for)h(an)g(Othello)f(and)h(a)g(check)o(ers)h(program,)i
1079 (and)244 4700 y(comparable)25 b(speedups)f(on)g(tw)o(o)h(chess)f
1080 (programs.)146 4969 y(Section)37 b(2)g(gi)n(v)o(es)e(a)j(brief)f(surv)o
1081 (e)o(y)e(of)i(rele)n(v)n(ant)f(parallel)h(search)g(methods.)66
1082 b(Section)37 b(3)g(describes)f(the)0 5169 y(APHID)26
1083 b(algorithm)e(in)i(detail,)f(along)g(with)g(an)h(illustrati)n(v)o(e)d
1084 (e)o(xample)i(of)g(ho)n(w)g(to)g(add)h(APHID)g(into)f(e)o(xisting)p
1085 0 5249 1560 4 v 112 5310 a Fj(2)149 5340 y Fi(It)c(is)g(freely)e(a)n(v)
1086 n(ailable)h(at)h Fh(http://www.cs.ualberta.ca/\230games/a)o(phid/)p
1087 Fi(.)1925 5589 y Fu(3)p eop
1089 4 6 bop 0 100 a Fu(sequential)28 b(game-tree)i(search)g(code.)45
1090 b(Section)29 b(4)g(sho)n(ws)f(the)i(e)o(xperimental)e(results)g(of)i
1091 (adding)f(APHID)g(to)0 299 y(four)c(applications.)k(Section)c(5)g
1092 (summarizes)e(this)h(paper)-5 b(.)0 637 y Fo(2)143 b(Pr)m(e)n(vious)34
1093 b(W)-11 b(ork)0 889 y Fg(2.1)119 b(The)30 b Ff(\013)q(\014)37
1094 b Fg(Algorithm)0 1156 y Fu(In)25 b(a)h(tw)o(o)e(player)i(zero-sum)f
1095 (game)f(with)h(perfect)g(information)f(and)h(a)h(\002nite)f(number)g
1096 (of)g(mo)o(v)o(es,)e(an)j(optimal)0 1355 y(strate)o(gy)g(can)h(be)g
1097 (determined)f(by)h(the)f(minimax)g(algorithm.)35 b(In)27
1098 b(general,)g(minimax)f(is)g(a)h(depth-\002rst)g(search)0
1099 1554 y(of)h(a)h(game)f(tree.)41 b(Each)29 b(node)f(represents)g(a)g
1100 (position,)g(and)g(the)g(links)f(between)h(nodes)g(represent)h(the)f
1101 (mo)o(v)o(e)0 1753 y(required)k(to)f(reach)h(the)g(ne)o(xt)e(position.)
1102 50 b(The)31 b(player)h(to)f(mo)o(v)o(e)f(alternates)h(at)h(each)g(le)n
1103 (v)o(el)f(of)g(the)h(tree.)51 b(The)0 1953 y(e)n(v)n(aluation)18
1104 b(of)i(each)h(leaf)g(node)f(in)f(the)h(search)h(is)f(based)g(on)f(an)i
1105 (approximation)d(of)i(whether)g(the)g(\002rst)g(player)h(is)0
1106 2152 y(going)f(to)h(win)g(the)h(game)e(\(heuristic)h(e)n(v)n(aluation)f
1107 (function\).)29 b(Whene)n(v)o(er)21 b(the)g(\002rst)g(player)h(mo)o(v)o
1108 (es,)e(he)i(chooses)0 2351 y(a)i(mo)o(v)o(e)f(to)g(maximize)g(his)h(e)n
1109 (v)n(aluation)e(\(so-called)h(Max)h(nodes)g(in)f(the)h(search)g
1110 (tree\).)31 b(Con)l(v)o(ersely)-6 b(,)23 b(when)h(the)0
1111 2550 y(second)i(player)g(has)h(to)f(mo)o(v)o(e)e(at)j(a)f(node,)h(he)f
1112 (will)g(choose)g(the)g(mo)o(v)o(e)f(that)h(minimizes)e(the)i(e)n(v)n
1113 (aluation)f(\(Min)0 2750 y(nodes\).)146 2949 y(Although)c(the)h(tree)g
1114 (is)g(\002nite,)g(it)g(can)g(get)g(quite)f(lar)n(ge.)30
1115 b(T)-8 b(o)22 b(search)h(a)f(tree)h(of)f(depth)f Fq(d)h
1116 Fu(and)g(with)f Fq(b)i Fu(branches)0 3148 y(at)35 b(e)n(v)o(ery)g
1117 (node,)j Fq(b)658 3112 y Fe(d)735 3148 y Fu(nodes)c(w)o(ould)h(be)h(e)n
1118 (v)n(aluated.)61 b(F)o(ortunately)-6 b(,)37 b(there)e(are)h
1119 (straightforw)o(ard)f(\223bounding\224)0 3347 y(techniques)e(that)g
1120 (can)h(pro)o(v)o(e)e(some)h(e)n(v)n(aluations)e(are)k(irrele)n(v)n
1121 (ant.)55 b(The)34 b(most)e(popular)h(of)h(these)f(is)g(the)h
1122 Fq(\013)q(\014)0 3547 y Fu(algorithm,)23 b(gi)n(v)o(en)h(in)g(Figure)h
1123 (1.)146 3746 y(The)k Fq(\013)q(\014)35 b Fu(algorithm)27
1124 b(only)h(considers)h(nodes)f(that)h(are)g(rele)n(v)n(ant)f(to)h(the)g
1125 (search)g(windo)n(w)f([)p Fq(\013)q Fu(,)i Fq(\014)6
1126 b Fu(].)43 b Fq(\013)30 b Fu(rep-)0 3945 y(resents)g(the)f(best)h(v)n
1127 (alue)f(that)h(the)g(side)f(to)h(mo)o(v)o(e)e(can)i(achie)n(v)o(e)g
1128 (thus)f(f)o(ar)h(in)g(the)g(search.)46 b(Additional)29
1129 b(search)0 4144 y(at)i(this)g(node)g(is)f(intended)h(to)g(\002nd)g(mo)o
1130 (v)o(es)e(that)i(impro)o(v)o(e)f(this)g(lo)n(wer)h(bound)f(\(i.e.)50
1131 b(ha)n(v)o(e)31 b(a)g(v)n(alue)g Fq(>)40 b(\013)q Fu(\).)49
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6831 b(s)25 b(tree)i(is)f(small)f(and)h(is)f(quickly)g(searched.)35
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6834 (required)i(to)f(get)g(a)h Fq(d)p Fu(-ply)f Fq(\013)q(\014)32
6835 b Fu(search)27 b(of)f(the)h(full)f(game)g(tree)0 697
6836 y(\002nished,)h(after)g(which)g(it)f(proceeds,)h(via)g(iterati)n(v)o(e)
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6838 (until)0 897 y(the)e(time)f(limit)f(e)o(xpires.)146 1096
6839 y(Each)28 b(sla)n(v)o(e)e(searches)h(its)f(pieces)h(of)g(w)o(ork)g
6840 Fl(\()p Fq(d)d Fk(\000)g Fq(d)1968 1060 y Fp(0)1991 1096
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6875 Fu(The)i(master)f(is)g(responsible)f(for)i(ensuring)f(that)g(the)h
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6878 l(,)g Fq(d)1329 4809 y Fp(0)1379 4846 y Fu(ply)-6 b(,)27
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6887 10 12 bop 146 100 a Fu(APHID)26 b(completes)d(a)j Fq(d)p
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6889 (follo)n(wing)e(steps:)120 407 y(1.)49 b(Ex)o(ecute)37
6890 b(a)h(quick)f(search)h(\(or)g Fm(pass)p Fu(\))f(of)h(the)f
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6900 b(W)-8 b(ait)24 b(for)i(ne)n(w)e(information)f(from)i(a)g(sla)n(v)o(e)f
6901 (process.)120 1735 y(5.)49 b(Go)25 b(to)f(step)g(1.)146
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6919 Fq(d)2979 3002 y Fp(0)3002 3039 y Fu(\))k(ply)g(itself.)30
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6924 Fq(d)3781 3401 y Fp(0)3804 3437 y Fl(\))p Fu(\),)0 3636
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6926 Fq(\013)q(\014)30 b Fu(search)c(windo)n(w)d(at)i(that)g(node)f(without)
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6937 b Fk(\000)h Fq(d)2181 4397 y Fp(0)2204 4433 y Fl(\))p
6938 Fu(-ply)j(search)h(result,)i(that)d(v)n(alue)g(is)h(used.)3740
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6940 Fq(d)d Fk(\000)h Fq(d)409 4596 y Fp(0)432 4633 y Fl(\))p
6941 Fu(-ply)i(result)g(is)g(una)n(v)n(ailable)f(because)h(the)h(sla)n(v)o
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6947 b Fu(search)c(windo)n(w)-6 b(,)32 b(then)g(the)g(algorithm)e(guesses)i
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6952 b(This)31 b(is)0 5312 y(discussed)20 b(in)g(Section)g(4.)1900
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7010 (implicitly)e(in)i(an)h(application-independent)0 4882
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9584 /Courier ff 180.00 scf sf
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9587 /Courier ff 180.00 scf sf
9589 gs 1 -1 sc (int sc;) col-1 sh gr
9590 /Courier ff 180.00 scf sf
9592 gs 1 -1 sc (int under;) col-1 sh gr
9593 /Courier ff 180.00 scf sf
9595 gs 1 -1 sc (/* move counter */) dup sw pop neg 0 rm col-1 sh gr
9596 /Courier ff 180.00 scf sf
9598 gs 1 -1 sc (/* score returned by search */) dup sw pop neg 0 rm col-1 sh gr
9599 /Courier ff 180.00 scf sf
9601 gs 1 -1 sc (/* alpha for move to be searched */) dup sw pop neg 0 rm col-1 sh gr
9602 /Courier ff 180.00 scf sf
9604 gs 1 -1 sc (/* beta for move to be searched */) dup sw pop neg 0 rm col-1 sh gr
9605 /Courier ff 180.00 scf sf
9607 gs 1 -1 sc (/* Generate hash value and key for this position */) col-1 sh gr
9608 /Courier ff 180.00 scf sf
9610 gs 1 -1 sc (/* Fetch information from transposition table */) col-1 sh gr
9611 /Courier ff 180.00 scf sf
9613 gs 1 -1 sc (if \(aphid_master\(\) == FALSE && h_length >= plytogo\) {) col-1 sh gr
9614 /Courier ff 180.00 scf sf
9616 gs 1 -1 sc (if \(flag == VALID\) { return\(h_score\); }) col-1 sh gr
9617 /Courier ff 180.00 scf sf
9619 gs 1 -1 sc (if \(flag == LBOUND\) { alpha = max\(alpha,h_score\); }) col-1 sh gr
9620 /Courier ff 180.00 scf sf
9622 gs 1 -1 sc (if \(flag == UBOUND\) { beta = min\(beta,h_score\); }) col-1 sh gr
9623 /Courier ff 180.00 scf sf
9625 gs 1 -1 sc (if \(alpha >= beta\) { return\(h_score\); }) col-1 sh gr
9626 /Courier ff 180.00 scf sf
9628 gs 1 -1 sc (}) col-1 sh gr
9629 /Courier ff 180.00 scf sf
9631 gs 1 -1 sc (/* Evaluate position if at bottom of tree */) col-1 sh gr
9632 /Courier ff 180.00 scf sf
9634 gs 1 -1 sc (/* If we have searched position deep enough, use score info */) col-1 sh gr
9635 /Courier ff 180.00 scf sf
9637 gs 1 -1 sc (if \(plytogo == 0\) { return\(Evaluate\(p\)\); }) col-1 sh gr
9638 /Courier ff 180.00 scf sf
9640 gs 1 -1 sc (generate_hash\(p, p_hash, p_key\);) col-1 sh gr
9641 /Courier ff 180.00 scf sf
9643 gs 1 -1 sc (retrieve\(p_hash, p_key, p_entry, h_length, h_score, h_flag, h_move\);) col-1 sh gr
9644 /Courier ff 180.00 scf sf
9646 gs 1 -1 sc (if \(aphid_horizon\(depth, plytogo, p_hash, p_key\) == TRUE\) {) col-1 sh gr
9647 /Courier ff 180.00 scf sf
9649 gs 1 -1 sc (return\(aphid_eval_leaf\(alpha, beta, depth, plytogo, p_hash, p_key\)\);) col-1 sh gr
9650 /Courier ff 180.00 scf sf
9652 gs 1 -1 sc (}) col-1 sh gr
9653 /Courier ff 180.00 scf sf
9655 gs 1 -1 sc (/* Generate move list, evaluate position if no moves */) col-1 sh gr
9656 /Courier ff 180.00 scf sf
9658 gs 1 -1 sc (numOfSuccessors = GenerateSuccessors\(p\);) col-1 sh gr
9659 /Courier ff 180.00 scf sf
9661 gs 1 -1 sc (if \(numOfSuccessors == 0\) { return\(Evaluate\(p\)\); }) col-1 sh gr
9662 /Courier ff 180.00 scf sf
9664 gs 1 -1 sc (if \(aphid_checkalarm\(FALSE\) != FALSE\) {) col-1 sh gr
9665 /Courier ff 180.00 scf sf
9667 gs 1 -1 sc (terminate_search = TRUE;) col-1 sh gr
9668 /Courier ff 180.00 scf sf
9670 gs 1 -1 sc (}) col-1 sh gr
9671 /Courier ff 180.00 scf sf
9673 gs 1 -1 sc (under = alpha; over = beta;) col-1 sh gr
9674 /Courier ff 180.00 scf sf
9676 gs 1 -1 sc (aphid_intnode_start\(depth, p_hash, p_key\);) col-1 sh gr
9677 /Courier ff 180.00 scf sf
9679 gs 1 -1 sc (if \(sc > under && i > 1 && sc < beta && plytogo > 2\) {) col-1 sh gr
9680 /Courier ff 180.00 scf sf
9682 gs 1 -1 sc (sc = -AlphaBeta\(p,-beta,-sc,plytogo-1\);) col-1 sh gr
9683 /Courier ff 180.00 scf sf
9685 gs 1 -1 sc (/* Is a research necessary? */) col-1 sh gr
9686 /Courier ff 180.00 scf sf
9688 gs 1 -1 sc (sc = -AlphaBeta\(p,-over,-under,plytogo-1\);) col-1 sh gr
9689 /Courier ff 180.00 scf sf
9691 gs 1 -1 sc (aphid_intnode_move\(depth, &\(movelist[i]\)\);) col-1 sh gr
9692 /Courier ff 180.00 scf sf
9694 gs 1 -1 sc (make_move\(p, movelist[i]\);) col-1 sh gr
9695 /Courier ff 180.00 scf sf
9697 gs 1 -1 sc (char *p_hash;) col-1 sh gr
9698 /Courier ff 180.00 scf sf
9700 gs 1 -1 sc (char *p_key;) col-1 sh gr
9701 /Courier ff 180.00 scf sf
9703 gs 1 -1 sc (int h_length;) col-1 sh gr
9704 /Courier ff 180.00 scf sf
9706 gs 1 -1 sc (int h_score;) col-1 sh gr
9707 /Courier ff 180.00 scf sf
9709 gs 1 -1 sc (int h_flag;) col-1 sh gr
9710 /Courier ff 180.00 scf sf
9712 gs 1 -1 sc (char *p_entry;) col-1 sh gr
9713 /Courier ff 180.00 scf sf
9715 gs 1 -1 sc (/* pointer to physical location of TT entry */) dup sw pop neg 0 rm col-1 sh gr
9716 /Courier ff 180.00 scf sf
9718 gs 1 -1 sc (/* pointer to hash value */) dup sw pop neg 0 rm col-1 sh gr
9719 /Courier ff 180.00 scf sf
9721 gs 1 -1 sc (/* pointer to hash table lock */) dup sw pop neg 0 rm col-1 sh gr
9722 /Courier ff 180.00 scf sf
9724 gs 1 -1 sc (/* ply position previously searched to */) dup sw pop neg 0 rm col-1 sh gr
9725 /Courier ff 180.00 scf sf
9727 gs 1 -1 sc (/* score at h_length ply from TT */) dup sw pop neg 0 rm col-1 sh gr
9728 /Courier ff 180.00 scf sf
9730 gs 1 -1 sc (/* type of score \(VALID, LBOUND or UBOUND\) */) dup sw pop neg 0 rm col-1 sh gr
9731 /Courier ff 180.00 scf sf
9733 gs 1 -1 sc (/* recommended move from TT */) dup sw pop neg 0 rm col-1 sh gr
9734 /Courier ff 180.00 scf sf
9736 gs 1 -1 sc (move h_move;) col-1 sh gr
9737 /Courier ff 180.00 scf sf
9739 gs 1 -1 sc (int over;) col-1 sh gr
9740 /Courier ff 180.00 scf sf
9742 gs 1 -1 sc (move move_opt;) col-1 sh gr
9743 /Courier ff 180.00 scf sf
9745 gs 1 -1 sc (/* current best move */) dup sw pop neg 0 rm col-1 sh gr
9746 /Courier ff 180.00 scf sf
9748 gs 1 -1 sc (aphid_intnode_update\(depth, value\);) col-1 sh gr
9749 /Courier ff 180.00 scf sf
9751 gs 1 -1 sc (move movelist[MAX_LEGAL_MOVES];) col-1 sh gr
9752 /Courier ff 180.00 scf sf
9754 gs 1 -1 sc (/* ordered list of all moves */) dup sw pop neg 0 rm col-1 sh gr
9755 /Courier ff 180.00 scf sf
9757 gs 1 -1 sc (/* total number of moves in movelist[] */) dup sw pop neg 0 rm col-1 sh gr
9758 /Courier ff 180.00 scf sf
9760 gs 1 -1 sc (/* current best minimax value */) dup sw pop neg 0 rm col-1 sh gr
9761 /Courier ff 180.00 scf sf
9763 gs 1 -1 sc (for\(i=1; \(i <= numOfSuccessors && score <= beta\); i++\) {) col-1 sh gr
9764 /Courier ff 180.00 scf sf
9766 gs 1 -1 sc (/* set window for next child */) col-1 sh gr
9767 /Courier ff 180.00 scf sf
9769 gs 1 -1 sc (under = max\(gamma, alpha\); over = under + 1;) col-1 sh gr
9770 /Courier ff 180.00 scf sf
9772 gs 1 -1 sc (}) col-1 sh gr
9773 /Courier ff 180.00 scf sf
9775 gs 1 -1 sc (/* Write information into transposition table */) col-1 sh gr
9776 /Courier ff 180.00 scf sf
9778 gs 1 -1 sc (if \(sc > gamma\) {) col-1 sh gr
9779 /Courier ff 180.00 scf sf
9781 gs 1 -1 sc (gamma = sc;) col-1 sh gr
9782 /Courier ff 180.00 scf sf
9784 gs 1 -1 sc (move_opt = movelist[i];) col-1 sh gr
9785 /Courier ff 180.00 scf sf
9787 gs 1 -1 sc (}) col-1 sh gr
9788 /Courier ff 180.00 scf sf
9790 gs 1 -1 sc (gamma = -INFINITY;) col-1 sh gr
9791 /Courier ff 180.00 scf sf
9793 gs 1 -1 sc (aphid_intnode_end\(depth, score, beta\); ) col-1 sh gr
9794 /Courier ff 180.00 scf sf
9796 gs 1 -1 sc (}) col-1 sh gr
9797 /Courier ff 180.00 scf sf
9799 gs 1 -1 sc (unmake_move\(p, movelist[i]\);) col-1 sh gr
9800 /Courier ff 180.00 scf sf
9802 gs 1 -1 sc (h_flag = VALID;) col-1 sh gr
9803 /Courier ff 180.00 scf sf
9805 gs 1 -1 sc (if \(score <= alpha\) { h_flag = LBOUND; }) col-1 sh gr
9806 /Courier ff 180.00 scf sf
9808 gs 1 -1 sc (if \(h_length <= plytogo\) {) col-1 sh gr
9809 /Courier ff 180.00 scf sf
9811 gs 1 -1 sc (if \(score >= beta\) { h_flag = UBOUND; }) col-1 sh gr
9812 /Courier ff 180.00 scf sf
9814 gs 1 -1 sc (}) col-1 sh gr
9815 /Courier ff 180.00 scf sf
9817 gs 1 -1 sc (p_entry = store\(p_hash, p_key, plytogo, score, h_flag, move_opt\);) col-1 sh gr
9818 /Courier ff 180.00 scf sf
9820 gs 1 -1 sc (} /* AlphaBeta */) col-1 sh gr
9821 /Courier ff 180.00 scf sf
9823 gs 1 -1 sc (int AlphaBeta\(position p, int alpha, int beta, int depth, int plytogo\) {) col-1 sh gr
9824 /Courier ff 180.00 scf sf
9826 gs 1 -1 sc (return\(0\); /* Should exit AlphaBeta quickly when alarm on */) col-1 sh gr
9827 /Courier ff 180.00 scf sf
9829 gs 1 -1 sc (return\(gamma\);) col-1 sh gr
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9837 (the)i Fq(\013)q(\014)30 b Fu(Algorithm)1900 5589 y(18)p
9840 19 21 bop 146 100 a Fu(It)23 b(should)f(also)h(be)g(noted)f(that,)h(in)
9841 g(terms)f(of)h(ease)h(of)f(use,)g(the)g(APHID)g(library)g(is)f(almost)g
9842 (unique.)29 b(Gi)n(v)o(en)0 299 y(an)22 b Fq(\013)q(\014)27
9843 b Fu(program)21 b(with)g(the)g(code)h(structured)f(to)g(use)g(the)h
9844 (Cilk)f(directi)n(v)o(es,)g(then)g(parallel)g Fm(sync)o(hr)l(onous)f
9845 Fu(search)0 498 y(algorithms,)f(such)g(as)h(YBWC)h(and)e(PV)-10
9846 b(-Split,)21 b(can)f(be)f(easily)h(implemented)e([1].)29
9847 b(Cilk)19 b(uses)g(multiple)f(threads)0 697 y(to)27 b(coordinate)g(the)
9848 g(search,)h(where)g(each)f(thread)h(represents)f(a)g(node)g(where)h(w)o
9849 (ork)f(has)g(been)g(split)f(of)n(f)h(from)0 897 y(its)d(parent.)0
9850 1236 y Fo(4)143 b(Experimental)33 b(Results)0 1539 y
9851 Fu(Most)c(authors)g(demonstrate)h(the)g(ef)n(fecti)n(v)o(eness)e(of)i
9852 (their)g(parallel)g(algorithm)f(using)g(a)h(single)f(application.)0
9853 1738 y(Chess)40 b(is)f(often)h(chosen)g(because)g(synchronous)f
9854 (algorithms)f(usually)h(yield)g(good)g(speedups)g(when)h(the)0
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9858 b(each)g(written)f(by)g(dif)n(ferent)g(authors)g(and)g(with)f(dif)n
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9868 b(results)g(are)h(presented)g(in)f(Section)h(4.3.)0 3428
9869 y Fg(4.1)119 b(Methodology)0 3694 y Fu(APHID)19 b(has)g(been)g
9870 (implemented)e(in)i(four)g(applications:)28 b(C)t Fa(H)t(I)t(N)t(O)t(O)
9871 t(K)r Fu(,)e(C)t Fa(R)t(A)t(F)t(T)t(Y)r Fu(,)h(K)t Fa(E)t(Y)-6
9872 b(A)t(N)t(O)25 b Fu(and)c(T)t Fa(H)t(E)t Fu(T)t Fa(U)t(R)t(K)r
9873 Fu(.)2 3893 y(C)t Fa(H)t(I)t(N)t(O)t(O)t(K)26 b Fu(is)20
9874 b(the)g(Man)g(vs.)28 b(Machine)20 b(W)-8 b(orld)20 b(Check)o(ers)h
9875 (Champion)e(program)h(\(principal)f(author:)28 b(Jonathan)0
9876 4093 y(Schaef)n(fer\).)37 b(K)t Fa(E)t(Y)-6 b(A)t(N)t(O)32
9877 b Fu(is)25 b(a)h(state-of-the-art)g(Othello)e(program,)i(which)f(rank)o
9878 (ed)h(among)f(the)h(top)f(\002)n(v)o(e)g(com-)0 4292
9879 y(puter)32 b(Othello)e(programs)h(w)o(orldwide)g(from)h(1992)f(to)g
9880 (1996)g(\(author:)44 b(Mark)32 b(Brockington\).)52 b(C)t
9881 Fa(R)t(A)t(F)t(T)t(Y)40 b Fu(is)0 4491 y(a)35 b(strong)f(free)n(w)o
9882 (are)i(chess)f(program)g(\(author:)51 b(Robert)35 b(Hyatt\).)63
9883 b(T)t Fa(H)t(E)t Fu(T)t Fa(U)t(R)t(K)42 b Fu(is)34 b(a)h(strong)g
9884 (chess)f(program)0 4690 y(designed)g(by)h(tw)o(o)g(graduate)g(students)
9885 f(at)h(the)g(Uni)n(v)o(ersity)e(of)i(Alberta)g(\(Andreas)g(Junghanns)f
9886 (and)h(Yngvi)0 4890 y(Bjornsson\).)63 b(Both)36 b(chess)g(programs)g
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9888 b(Computer)f(Chess)h(Champi-)0 5089 y(onsip.)52 b(All)32
9889 b(of)g(the)g(applications)f(ha)n(v)o(e)h(a)h(\002nely-tuned)f
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9893 (search)f(trees)h(that)1900 5589 y(19)p eop
9895 20 22 bop 0 100 a Fu(are)26 b(close)e(to)h(the)f(critical)h(tree)g(in)f
9896 (size.)146 299 y(All)g(e)o(xperiments)f(were)j(performed)e(on)g(a)h
9897 (Silicon)f(Graphics)h(Origin)e(2000)h(with)g(64)g(processors.)3631
9898 263 y Fn(6)3701 299 y Fu(Each)0 498 y(of)34 b(the)g(applications)e
9899 (were)j(compiled)e(with)g(SGI')-5 b(s)34 b Fb(cc)g Fu(compiler)-5
9900 b(.)57 b(F)o(or)34 b(the)g(parallel)g(tests,)h(tw)o(o)e(dif)n(ferent)0
9901 697 y(v)o(ersions)h(of)i(the)g(code)g(were)g(compiled.)62
9902 b(The)36 b(\002rst)g(parallel)f(program)h(could)f(be)h(used)f(at)h
9903 (run-time)f(as)h(a)0 897 y(master)30 b(or)g(a)g(sla)n(v)o(e)g(by)f
9904 (APHID.)i(The)f(second)g(program)g(w)o(as)g(an)g(e)o(x)o(ecutable)f
9905 (that)h(could)f(only)g(be)i(used)e(by)0 1096 y(APHID)34
9906 b(as)f(a)h(sla)n(v)o(e.)55 b(This)33 b(separation)g(impro)o(v)o(ed)e
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9908 1295 y(used)25 b(only)f(by)g(the)h(master)f(impacted)g(the)h
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9910 Fq(\013)q(\014)30 b Fu(algorithm.)146 1494 y(P)o(arallel)i(and)g
9911 (sequential)f(algorithms)f(often)h(do)h(not)f(agree)i(with)e(each)h
9912 (other)f(about)h(the)f(search)i(result)0 1694 y(\(v)n(alue)24
9913 b(and/or)g(best)g(mo)o(v)o(e\))f(when)h(the)h(full)f(v)o(ersion)f(of)h
9914 (the)h(program)f(is)g(used)g([12].)31 b(F)o(or)24 b(e)o(xample,)f(dif)n
9915 (ferent)0 1893 y(search)g(windo)n(ws)e(can)i(cause)g(dif)n(ferent)f
9916 (search)h(e)o(xtensions)e(to)h(be)g(turned)h(on,)f(resulting)g(in)g(a)h
9917 (dif)n(ferent)f(v)n(alue)0 2092 y(at)33 b(the)h(root.)56
9918 b(One)33 b(w)o(ould)g(prefer)h(that)f(the)g(parallel)g(and)h
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9924 b(As)29 b(a)g(compromise,)f(most)g(of)0 2690 y(the)20
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9928 b(This)21 b(does)i(not)f(imply)f(that)h(a)h(\002x)o(ed)f(search)h
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9931 g(programs)f(still)g(used)g(quiescence)h(search)h(to)e(e)o(xtend)g(the)
9932 h(search)g(well)0 3288 y(be)o(yond)24 b(the)g Fq(d)p
9933 Fu(-ply)g(search)i(horizon.)146 3487 y(The)g(size)f(of)g(each)h(of)g
9934 (the)f(searches)h(is)f(important)e(to)i(the)g(observ)o(ed)g(speedup.)32
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9938 b(Ho)n(we)n(v)o(er)l(,)21 b(searching)h(game)g(trees)g(that)g(occur)g
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9943 o(erage)h(time)f(spent)g(searching)h(on)f(a)h(64-processor)g(machine)f
9944 (did)g(not)g(e)o(xceed)h(the)0 4483 y(usual)e(time)h(controls)f(in)g
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9946 (chess,)h(60)g(seconds)g(in)f(Othello,)0 4682 y(and)29
9947 b(120)g(seconds)g(in)f(the)h(game)g(of)g(check)o(ers.)45
9948 b(Consequently)-6 b(,)29 b(the)g(search)g(depth)g(achie)n(v)o(ed)f
9949 (depended)h(on)0 4882 y(the)f(game)g(being)g(studied)f(and)i(the)f
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9951 (search)g(depth)e(v)n(aried)h(from)0 5081 y(25)h(to)f(29)h(ply)-6
9952 b(,)29 b(while)f(for)h(chess)g(it)g(w)o(as)g(11)f(or)i(12)e(ply)-6
9953 b(.)42 b(F)o(or)29 b(Othello,)g(all)g(positions)e(were)i(searched)h(15)
9954 f(ply)p 0 5171 1560 4 v 112 5232 a Fj(6)149 5262 y Fi(Additional)19
9955 b(e)o(xperiments)g(ha)n(v)o(e)g(been)h(done)f(using)h(Sun)g(equipment)e
9956 (to)i(test)h(the)f(portability)f(of)h(the)g(APHID)h(library)e([2)o(].)
9957 1900 5589 y Fu(20)p eop
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9960 n(aried)g(from)g(4)h(to)f(8)g(ply)g(\(4)h(in)f(chess)h(and)f(Othello,)i
9961 (6)f(to)f(8)g(ply)g(in)0 299 y(check)o(ers\).)63 b(A)36
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9967 f([2].)146 897 y(Using)j(a)g(transposition)e(table)i(that)g(is)g(lar)n
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9972 (that)g(this)h(limitation)e(w)o(ould)h(dramatically)g(af)n(fect)i(the)f
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10000 f(the)g(scalability)g(of)h(memory)-6 b(.)32 b(Other)25
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10002 4284 y(entries)34 b(to)g(increase)h(in)f(tandem)g(with)g(the)g(number)g
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10010 (should)e(a)n(v)n(oid)g(directly)g(comparing)g(speedups)h(without)0
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12425 b(I,)h(sho)n(w)e(that)g(the)h(APHID)g(algorithm)e(can)j(deli)n(v)o(er)d
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12429 y(since)h(APHID)g(is)f(easy)h(to)g(inte)o(grate)f(into)g(an)g(e)o
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12431 1398 y(Comparing)31 b(APHID)g(to)g(synchronous)f(approaches,)i(it)f(is)
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12436 b(a)d(lar)n(ger)g(branching)e(f)o(actor)i(yields)e(more)h(parallelism)f
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12444 (chess.)29 b(Thus,)23 b(a)g(synchronous)f(parallel)h(algorithm)e(may)i
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12448 (e)o(xisting)e(le)o(gac)o(y)h(code,)i(\(2\))f(can)h(lik)o(ely)e(achie)n
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12450 (table)h(memory)-6 b(,)23 b(and)h(\(3\))g(has)g(the)g(additional)e
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12453 (depth,)g(then)f(APHID)h(becomes)g(the)f(algorithm)g(of)h(choice.)146
12454 3590 y(It)h(is)g(hoped)g(that)f(this)g(document,)h(in)f(conjunction)g
12455 (with)g(the)h(freely-a)n(v)n(ailable)g(APHID)g(library)-6
12456 b(,)26 b(will)f(be)0 3789 y(helpful)32 b(for)i(game-tree)f(researchers)
12457 h(to)f(in)l(v)o(estigate)e(these)i(and)g(other)g(ideas)f(surrounding)g
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12459 y Fo(6)143 b(Ackno)o(wledgements)0 4630 y Fu(P)o(aul)20
12460 b(Masiar)g(and)h(Marc)g(Nolte)e(arranged)i(access)g(to)f(the)h
12461 (64-processor)f(SGI)h(Origin)f(2000)f(system)h(in)g(Eagan,)0
12462 4830 y(Minnesota.)28 b(Charles)20 b(Leiserson,)h(Ask)o(e)f(Plaat)g(and)
12463 g(Boston)g(Uni)n(v)o(ersity)e(arranged)j(access)f(to)g(a)g
12464 (32-processor)0 5029 y(SGI)30 b(Origin)e(2000)g(system.)43
12465 b(The)29 b(authors)f(w)o(ould)g(also)h(lik)o(e)f(to)h(thank)g(Darse)g
12466 (Billings,)g(Yngvi)f(Bj)8 b(\250)-41 b(ornsson,)0 5228
12467 y(Murray)38 b(Campbell,)k(Joe)c(Culberson,)j(Y)-10 b(aoqing)38
12468 b(Gao,)k(Andreas)d(Junghanns,)h(T)-8 b(on)o(y)37 b(Marsland,)42
12469 b(Monroe)1900 5589 y(30)p eop
12471 31 33 bop 0 100 a Fu(Ne)n(wborn,)24 b(Denis)g(P)o(app,)h(John)f
12472 (Samson,)g(and)h(the)g(referees)h(for)f(their)f(helpful)h(suggestions.)
12473 0 436 y Fo(Refer)m(ences)50 738 y Fu([1])49 b(R.)31 b(D.)f(Blumofe,)i
12474 (C.)f(F)-8 b(.)31 b(Joer)n(g,)h(B.)g(C.)f(K)o(uszmaul,)f(C.)h(E.)g
12475 (Leiserson,)g(K.)g(H.)f(Randall,)i(and)f(Y)-13 b(.)31
12476 b(Zhou.)215 938 y(Cilk:)51 b(An)35 b(Ef)n(\002cient)g(Multithreaded)f
12477 (Runtime)h(System.)69 b(In)35 b Fm(Pr)l(oceedings)f(of)h(PPOPP)g('95)p
12478 Fu(,)j(pages)215 1137 y(207\226216,)23 b(Santa)j(Barbara,)g(CA,)f(July)
12479 f(1995.)50 1413 y([2])49 b(M.)36 b(G.)i(Brockington.)74
12480 b Fm(Async)o(hrnous)36 b(P)-8 b(ar)o(allel)35 b(Game-T)-5
12481 b(r)l(ee)38 b(Sear)l(c)o(h)p Fu(.)75 b(PhD)37 b(thesis,)i(Uni)n(v)o
12482 (ersity)c(of)215 1612 y(Alberta,)24 b(Department)h(of)f(Computing)g
12483 (Science,)h(Edmonton,)e(Canada,)j(December)f(1997.)50
12484 1889 y([3])49 b(R.)32 b(Feldmann.)59 b Fm(Spielbaumsuc)o(he)31
12485 b(auf)g(Massiv)h(P)-8 b(ar)o(allelen)30 b(Systemen)p
12486 Fu(.)60 b(PhD)32 b(thesis,)h(Uni)n(v)o(ersity)d(of)215
12487 2088 y(P)o(aderborn,)22 b(P)o(aderborn,)f(German)o(y)-6
12488 b(,)21 b(May)g(1993.)27 b(English)20 b(translation)g(a)n(v)n(ailable:)
12489 27 b(Game)22 b(T)m(ree)f(Search)215 2287 y(on)j(Massi)n(v)o(ely)f(P)o
12490 (arallel)i(Systems.)50 2564 y([4])49 b(A.)25 b(Geist,)f(A.)h(Be)o
12491 (guelin,)g(J.)g(Dongarra,)g(W)-9 b(.)25 b(Jiang,)f(B.)i(Manchek,)f(and)
12492 g(V)-13 b(.)25 b(Sunderam.)37 b Fm(PVM:)25 b(P)-8 b(ar)o(allel)215
12493 2763 y(V)h(irtual)33 b(Mac)o(hine)i(\226)h(A)f(User')l(s)g(Guide)g(and)
12494 h(T)-5 b(utorial)33 b(for)i(Network)o(ed)i(P)-8 b(ar)o(allel)33
12495 b(Computing)p Fu(.)69 b(MIT)215 2962 y(Press,)25 b(1994.)50
12496 3238 y([5])49 b(R.)36 b(D.)g(Greenblatt,)j(D.)d(E.)f(Eastlak)o(e,)k
12497 (and)d(S.)g(D.)g(Crock)o(er)-5 b(.)72 b(The)36 b(Greenblatt)g(Chess)g
12498 (Program.)72 b(In)215 3438 y Fm(Pr)l(oceedings)23 b(of)i(the)f(F)-7
12499 b(all)24 b(J)n(oint)f(Computer)i(Confer)l(ence)p Fu(,)g(v)n(olume)f
12500 (31,)g(pages)h(801\226810,)f(1967.)50 3714 y([6])49 b(R.)34
12501 b(M.)f(Hyatt.)63 b Fm(A)33 b(High-P)-8 b(erformance)33
12502 b(P)-8 b(ar)o(allel)31 b(Algorithm)h(T)-9 b(o)34 b(Sear)l(c)o(h)f
12503 (Depth-F)l(ir)o(st)e(Game)j(T)-5 b(r)l(ees)p Fu(.)215
12504 3913 y(PhD)25 b(thesis,)f(Uni)n(v)o(ersity)e(of)j(Alabama,)f
12505 (Birmingham,)g(Alabama,)g(1988.)50 4190 y([7])49 b(R.)22
12506 b(M.)f(Hyatt.)28 b(The)22 b(Dynamic)f(T)m(ree)g(Splitting)f(P)o
12507 (arallel)i(Search)h(Algorithm.)k Fm(ICCA)22 b(J)n(ournal)p
12508 Fu(,)f(20\(1\):3\226)215 4389 y(19,)j(1997.)50 4665 y([8])49
12509 b(A.)24 b(Junghanns)e(and)j(J.)e(Schaef)n(fer)-5 b(.)35
12510 b(Search)25 b(V)-11 b(ersus)24 b(Kno)n(wledge)f(in)h(Game-Playing)f
12511 (Programs)h(Re)n(vis-)215 4864 y(ited.)35 b(In)25 b Fm(Pr)l(oceedings)e
12512 (of)i(IJCAI-97)p Fu(,)g(pages)g(692\226697,)f(Nago)o(ya,)g(Japan,)h
12513 (August)f(1997.)50 5141 y([9])49 b(D.)29 b(E.)f(Knuth)g(and)h(R.)h(W)-9
12514 b(.)28 b(Moore.)49 b(An)28 b(Analysis)g(of)h(Alpha-Beta)g(Pruning.)49
12515 b Fm(Arti\002cial)27 b(Intellig)o(ence)p Fu(,)215 5340
12516 y(6\(3\):293\226326,)c(1975.)1900 5589 y(31)p eop
12518 32 34 bop 0 100 a Fu([10])49 b(D.)23 b(K)m(opec)g(and)g(I.)h(Bratk)o
12519 (o.)33 b(The)23 b(Bratk)o(o-K)m(opec)h(Experiment:)k(A)c(Comparison)e
12520 (of)i(Human)f(and)g(Com-)215 299 y(puter)g(Performance)h(in)f(Chess.)32
12521 b(In)23 b(M.R.B.)g(Clark)o(e,)h(editor)l(,)f Fm(Advances)g(in)g
12522 (Computer)g(Chess)g(3)p Fu(,)g(pages)215 498 y(57\22672.)h(Permagon)h
12523 (Press,)g(1982.)0 780 y([11])49 b(B.)28 b(C.)h(K)o(uszmaul.)44
12524 b(The)28 b(StarT)-7 b(ech)29 b(Massi)n(v)o(ely-P)o(arallel)d(Chess)i
12525 (Program.)46 b Fm(ICCA)29 b(J)n(ournal)p Fu(,)e(18\(1\):3\226)215
12526 980 y(19,)d(1995.)0 1262 y([12])49 b(C.-P)-11 b(.)30
12527 b(P)-11 b(.)30 b(Lu.)51 b(P)o(arallel)29 b(Search)i(of)e(Narro)n(w)h
12528 (Game)f(T)m(rees.)51 b(Master')-5 b(s)29 b(thesis,)g(Uni)n(v)o(ersity)f
12529 (of)h(Alberta,)215 1461 y(Department)24 b(of)h(Computing)e(Science,)j
12530 (Edmonton,)d(Canada,)i(1993.)0 1743 y([13])49 b(T)-7
12531 b(.)24 b(A.)h(Marsland)f(and)g(M.)h(S.)g(Campbell.)35
12532 b(P)o(arallel)25 b(Search)h(of)e(Strongly)g(Ordered)i(Game)e(T)m(rees.)
12533 36 b Fm(A)m(CM)215 1943 y(Computing)23 b(Surve)m(ys)p
12534 Fu(,)i(14\(4\):533\226551,)e(1982.)0 2225 y([14])49 b(M.)28
12535 b(M.)h(Ne)n(wborn.)48 b(Unsynchronized)28 b(Iterati)n(v)o(ely)f
12536 (Deepening)i(P)o(arallel)g(Alpha-Beta)g(Search.)50 b
12537 Fm(IEEE)215 2424 y(T)-5 b(r)o(ansactions)22 b(on)j(P)-8
12538 b(attern)23 b(Analysis)h(and)g(Mac)o(hine)g(Intellig)o(ence)p
12539 Fu(,)g(P)-9 b(AMI-10\(5\):687\226694,)23 b(1988.)0 2707
12540 y([15])49 b(J.)23 b(Schaef)n(fer)-5 b(.)33 b(Distrib)n(uted)21
12541 b(Game-T)m(ree)j(Searching.)32 b Fm(J)n(ournal)22 b(of)h(P)-8
12542 b(ar)o(allel)21 b(and)i(Distrib)n(uted)e(Comput-)215
12543 2906 y(ing)p Fu(,)j(6\(2\):90\226114,)f(1989.)0 3188
12544 y([16])49 b(J.)24 b(J.)g(Scott.)35 b(A)25 b(Chess-Playing)f(Program.)35
12545 b(In)25 b(B.)g(Meltzer)g(and)f(D.)g(Michie,)g(editors,)g
12546 Fm(Mac)o(hine)g(Intelli-)215 3387 y(g)o(ence)h(4)p Fu(,)g(pages)f
12547 (255\226265.)g(Edinb)n(ur)n(gh)g(Uni)n(v)o(ersity)e(Press,)j(1969.)0
12548 3670 y([17])49 b(J.-C.)35 b(W)-8 b(eill.)67 b Fm(Pr)l(o)o(gr)o(ammes)32
12549 b(d')1389 3648 y(\264)1369 3670 y(Ec)o(hecs)j(de)f(Championnat:)50
12550 b(Ar)l(c)o(hitectur)l(e)34 b(Lo)o(gicielle)o(,)j(Synth)3650
12551 3671 y(\036)3645 3670 y(ese)d(de)215 3869 y(F)-10 b(onctions)23
12552 b(d')730 3847 y(\264)711 3869 y(Evaluations,)f(P)-8 b(ar)o(all)1488
12553 3870 y(\264)1483 3869 y(elisme)23 b(de)i(Rec)o(her)l(c)o(he)p
12554 Fu(.)35 b(PhD)25 b(thesis,)e(Uni)n(v)o(ersit)6 b(\264)-39
12555 b(e)23 b(P)o(aris)i(8,)f(January)215 4068 y(1995.)35
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12558 (of)g(the)h(information)d(about)i(the)g(pre)n(vious)f(depths)h(of)g
12559 Fq(\013)q(\014)43 b Fu(search)38 b(for)f(a)h(node,)i(such)d(as)0
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12564 i(as)e(well)g(as)g(a)h(hypothetical)0 5308 y(minimax)28
12565 b(v)n(alue)h(for)g(the)h(current)g Fq(d)p Fu(-ply)e(search)i(\(the)g
12566 (closest)f(node)g(on)g(the)g(principal)g(v)n(ariation)f(that)h(has)h(a)
12567 1900 5589 y(32)p eop
12569 33 35 bop 0 100 a Fu(certain)28 b(v)n(alue\).)38 b(All)27
12570 b(of)h(this)f(information)f(is)h(used)g(to)g(determine)g(a)h(guessed)f
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12572 (Figure)g(10.)146 498 y(Starting)i(with)f(the)g(information)g(for)h(a)g
12573 Fl(\()p Fq(d)c Fk(\000)h Fq(d)1817 462 y Fp(0)1863 498
12574 y Fk(\000)g Fl(1\))p Fu(-ply)i(search,)i(the)f(algorithm)e(checks)i
12575 (successi)n(v)o(ely)0 697 y(shallo)n(wer)e(depths)g(of)h(search)g
12576 (returned)g(by)g(the)f(sla)n(v)o(e)h(until)e(a)j(rele)n(v)n(ant)d
12577 (result)i(is)f(found)h(with)f(respect)h(to)f(the)0 897
12578 y Fq(\013)q(\014)33 b Fu(search)28 b(windo)n(w)-6 b(.)36
12579 b(This)26 b(is)h(guaranteed)h(to)f(happen,)g(since)g(the)h(master)f
12580 (stores)f(an)i(e)o(xact)f(e)n(v)n(aluation)e(of)j(a)0
12581 1096 y(leaf)d(node)g(\(a)g(0-ply)f(search\))i(when)f(the)f(leaf)h(is)g
12582 (\002rst)g(generated)g(and)g(gi)n(v)o(en)e(to)h(a)i(sla)n(v)o(e.)146
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12584 n(v)o(e)g(should)f(not)h(be)g(used)h(without)e(an)h(adjustment)f(since)
12585 h(the)0 1494 y(minimax)24 b(v)n(alue)h(at)h(the)g(root)f(of)h(the)g
12586 (tree)g(may)g(v)n(ary)f(between)h(dif)n(ferent)g(depths)f(of)h(search.)
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12588 b(minimax)g(v)n(alue)h(is)g(scaled)h(by)f(the)g(dif)n(ference)h
12589 (between)g(the)f(v)n(alue)g(of)h(the)f(full)g(search)h(that)f(it)g(w)o
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12592 (current)h(search)0 2092 y(has)k(a)g(hypothetical)d(minimax)h(v)n(alue)
12593 h(of)h(5,)i(and)d(the)h(result)f(of)h Fk(\024)g Fu(6)f(from)h(a)g
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12595 (the)h(root)f(of)h(the)g(game)f(tree)h(is)f(to)h(be)g(used,)h(then)f
12596 (the)f(dif)n(ference)h(of)g(the)g(minimax)e(v)n(alues)0
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12598 b(Thus,)25 b(the)g(v)n(alue)g(changes)h(from)f Fk(\024)h
12599 Fu(6)g(for)g(the)f(earlier)i(search)f(to)f Fk(\024)h
12600 Fu(4)0 2690 y(for)g(use)g(as)f(a)h(guessed)f(minimax)g(v)n(alue)g(in)g
12601 (the)g(current)h(search.)34 b(This)25 b(preserv)o(es)h(the)f(mo)o(v)o
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12603 3088 y(This)c(algorithm)e(is)i(preferred)h(o)o(v)o(er)e(other)h
12604 (methods)f(for)h(determining)f(an)h(estimated)f(e)n(v)n(aluation)g
12605 (because)0 3288 y(it)k(guarantees)g(that)g(a)h(guessed)e(score)i(will)e
12606 (not)h(disrupt)f(the)h(search)h(tree.)31 b(If)23 b(the)g(old)g(search)h
12607 (result)f(\()p Fk(\024)h Fu(6\))f(w)o(as)0 3487 y(suf)n(\002cient)g(to)
12608 h(cause)h(the)e(tree)i(to)f(be)g(pruned)g(in)f(the)h(earlier)h(search,)
12609 f(the)g(guessed)g(v)n(alue)f(\()p Fk(\024)29 b Fl(4)p
12610 Fu(\))24 b(will)f(lik)o(ely)g(be)0 3686 y(suf)n(\002cient)h(to)h(prune)
12611 f(the)h(tree)g(in)g(the)f(current)h(search.)0 4026 y
12612 Fo(B)143 b(The)35 b(Sla)l(v)o(e')-5 b(s)34 b(W)m(indo)o(w)h(Selection)f
12613 (Algorithm)0 4328 y Fu(The)29 b(windo)n(w)f(selection)g(algorithm)g(is)
12614 g(application-dependent,)h(and)g(can)g(be)g(modi\002ed)g(by)g(editing)f
12615 (a)h(call-)0 4527 y(back)f(function)f(pro)o(vided)g(to)g(the)h
12616 (application)f(programmer)-5 b(.)38 b(Based)29 b(on)e(numerous)g
12617 (tests,)h(a)g(general)g(set)g(of)0 4727 y(rules)d(w)o(as)f(created)i
12618 (for)f(determining)e(small,)h(useful)g Fq(\013)q(\014)31
12619 b Fu(search)25 b(windo)n(ws)e(in)i(APHID.)146 4926 y(The)39
12620 b(\002rst)f(recommendation)f(is)h(that)g(the)g(sla)n(v)o(e')-5
12621 b(s)38 b(search)g(windo)n(w)f(should)h(be)g(centered)h(around)f(the)0
12622 5125 y(hypothetical)29 b(minimax)g(v)n(alue)i(\(as)g(de\002ned)g(in)g
12623 (Section)f(3.1\),)i(since)f(this)f(is)h(the)f(most)g(lik)o(ely)g(v)n
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projects / typhoon-papers.git / blob