%!PS-Adobe-2.0 %%Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %%Title: acm.dvi %%Pages: 8 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%EndComments %DVIPSCommandLine: dvips -f acm.dvi %DVIPSParameters: dpi=600, comments removed %DVIPSSource: TeX output 1995.12.14:1155 %%BeginProcSet: tex.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if} forall round exch round exch]setmatrix}N /@landscape{/isls true N}B /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 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Fm( )e Fo(0;)-53 2405 y Fq(22)326 b Fp(alldone)21 b Fm( )e Fl(false)o Fo(;)-53 2479 y Fq(24)326 b Fp(while)p 329 2492 150 4 v 24 w Fo(\()p Fp(iteration)22 b Fn(<)d Fo(2\))32 b Fm(^)g Fo(\()p Fn(\013)20 b(<)g(\014)s Fo(\))32 b Fm(^)f(:)p Fp(alldone)25 b(do)p 1667 2492 72 4 v -53 2554 a Fq(25)499 b Fp(iteration)21 b Fm( )f Fp(iteration)d Fo(+)f(1;)-53 2629 y Fq(26)499 b Fp(alldone)21 b Fm( )e Fl(true)p Fo(;)-53 2704 y Fq(28)499 b Fn(M)27 b Fm( )19 b Fp(FirstMove)p Fo(\()p Fp(P)n(osition)r Fo(\);)-53 2778 y Fq(30)499 b Fp(while)p 502 2791 150 4 v 24 w Fo(\()p Fn(M)27 b Fm(6)p Fo(=)20 b(0)31 b Fm(^)h Fn(\013)20 b(<)f(\014)s Fo(\))24 b Fp(do)p 1250 2791 72 4 v -53 2853 a Fq(31)672 b Fp(exclusive)20 b Fm( )f Fo(\()p Fp(iteration)j Fo(=)e(1\))-53 2928 y Fq(32)684 b Fm(^)31 b Fo(\()p Fp(NotFirstMove)r Fo(\()p Fn(M)7 b Fo(\)\);)-53 3002 y Fq(34)672 b Fo(On)24 b(the)g(\014rst)g(iteration,)g(w)n(e)g(w)n(an)n(t)-53 3077 y Fq(35)672 b Fo(to)25 b(b)r(e)f(the)g(only)g(pro)r(cessor)-53 3152 y Fq(36)672 b Fo(to)25 b(ev)l(aluate)g(y)n(oung)g(sons.)-53 3227 y Fq(38)672 b Fp(value)20 b Fm( )f(\000)p Fp(ab)r(dada)q Fo(\()p Fp(P)n(osition)e Fm(\017)f Fn(M)s(;)c Fm(\000)p Fn(\014)s(;)-53 3301 y Fq(39)672 b Fm(\000)12 b Fo(max)o(\()p Fn(\013;)g Fp(Best)q Fo(\))p Fn(;)g Fp(depth)18 b Fm(\000)e Fo(1)p Fn(;)11 b Fp(exclusive)p Fo(\);)-53 3376 y Fq(40)672 b Fp(if)p 675 3389 39 4 v 23 w(value)20 b Fo(=)f Fm(\000)p Fp(ON)p 1143 3376 22 4 v 26 w(EV)-6 b(ALUA)g(TION)-53 3451 y Fq(41)734 b Fp(then)p 737 3464 130 4 v 25 w(alldone)21 b Fm( )e Fl(false)p Fo(;)-53 3526 y Fq(42)672 b Fp(elsif)p 675 3539 114 4 v 23 w(value)20 b Fn(>)g Fp(Best)-53 3600 y Fq(43)809 b Fp(then)p 812 3613 130 4 v 26 w(Best)20 b Fm( )f Fp(value)p Fo(;)-53 3675 y Fq(44)963 b Fp(if)p 966 3688 39 4 v 23 w(Best)20 b Fm(\025)g Fn(\014)-53 3750 y Fq(45)1025 b Fp(then)p 1028 3763 130 4 v 25 w Fl(skip)23 b Fp(endsea)n(rch)s Fo(;)42 b Fp(\014)p 1696 3763 38 4 v -53 3824 a Fq(46)672 b Fp(\014)p 675 3837 V -53 3899 a Fq(47)g 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Ft(exclusiveP)j Fx(is)f Ft(true)p Fx(.)54 b(Otherwise,)34 b(if)f(there)e(is)2241 625 y(no)23 b(forw)n(ard)h(pruning)f(due)f(to)h(the)g(transp)r(osition)h(table,)g (the)2241 708 y(en)n(try)h Ft(nproc)h Fx(is)h(incremen)n(ted.)2164 834 y Fu(\017)39 b Fx(Using)29 b(the)f(same)g(metho)r(d,)h(the)f (storing)i(pro)r(cedure)e(decre-)2241 918 y(men)n(ts)20 b(the)i(en)n(try)e Ft(nproc)j Fx(when)e(a)h(pro)r(cessor)i(lea)n(v)n (es)e(a)g(no)r(de.)2164 1044 y Fu(\017)39 b Fx(The)30 b(three)h(phases)f(are)h(implemen)n(ted)d(using)j(the)e(v)l(ariable) 2241 1127 y Ft(iteration)37 b Fx(whic)n(h)f(can)f(tak)n(e)h(the)f(v)l (alue)g Ft(1)g Fx(and)g Ft(2)h Fx(in)f(the)2241 1210 y(inner)f(lo)r(op)i(\(lines)f(29)g(to)g(42\).)62 b(The)35 b(\014rst)f(time)g(w)n(e)h(en)n(ter)2241 1293 y(the)g(inner)g(lo)r(op,) j(w)n(e)e(reset)g(the)e Ft(exclusive)j Fx(\015ag)f(only)f(on)2241 1376 y(the)29 b(\014rst)g(mo)n(v)n(e)f(while)j(w)n(e)e(reset)h(it)g(on) f(ev)n(ery)g(mo)n(v)n(e)f(in)h(the)2241 1459 y(second)34 b(iteration.)60 b(When)33 b(the)g Ft(exclusive)j Fx(\015ag)e(is)g(set,) j(a)2241 1542 y(son)26 b(whic)n(h)f(has)g(b)r(een)g(pruned)f(b)r (ecause)i(another)f(pro)r(cessor)2241 1625 y(is)35 b(curren)n(tly)e(ev) l(aluating)h(it)h(will)g(ha)n(v)n(e)f(a)g(return)f(v)l(alue)h(of)2241 1708 y Ft(-ON)p 2363 1708 V 29 w(EVALUATION)p Fx(.)e(If)e(w)n(e)g (\014nd)f(suc)n(h)h(a)g(son,)h(then)e(w)n(e)h(reset)2241 1791 y(the)i Ft(alldone)h Fx(\015ag)g(meaning)e(that)h(another)g (iteration)i(will)2241 1874 y(b)r(e)26 b(necessary)g(to)g(kno)n(w)f (the)g(v)l(alue)h(of)g(this)g(son.)2164 2061 y(With)g(this)f (de\014nition,)h(w)n(e)g(can)g(easily)h(see)f(that)g(compared)f(to)2049 2144 y(a)h(YBW)n(C)g(searc)n(h,)h(the)f(ABD)n(AD)n(A)e(searc)n(h)i (will)i(attempt)d(to)h(read)2049 2227 y(the)34 b(transp)r(osition)h (table)g(at)f(most)g(t)n(wice)h(as)g(man)n(y)d(times,)k(and)2049 2310 y(write)26 b(roughly)g(the)f(same)h(n)n(um)n(b)r(er)d(of)k(times.) 2049 2590 y Fy(3)100 b(RESUL)-8 b(TS)33 b(FROM)h(EXPERIMENTS)2049 2816 y Fx(T)-6 b(o)22 b(analyse)f(the)g(b)r(eha)n(viour)g(of)h(the)f (parallel)h(sc)n(heme,)g(w)n(e)f(used)g(the)2049 2899 y(parallelization)26 b(of)e(t)n(w)n(o)g(sequen)n(tial)g(game)f (programs:)34 b(a)24 b(comp)r(eti-)2049 2982 y(tiv)n(e)g(Othello)g (program)2750 2950 y Fv(3)2809 2982 y Fx(and)g(an)g(early)g(v)n(ersion) h(of)g(the)e Fs(F)-6 b(r)l(enchess)2049 3065 y Fx(c)n(hess)26 b(program.)2164 3212 y(The)34 b(Othello)h(program)f(has)g(an)g (unstable)g(ev)l(aluation)g(func-)2049 3295 y(tion)c(as)h(the)e(searc)n (h)h(is)h(extended.)46 b(Most)30 b(Othello)h(programmers)2049 3378 y(kno)n(w)k(of)h(the)e(o)r(dd{ev)n(en)h(problem)f(whic)n(h)h (results)h(in)f(an)g(ev)l(alu-)2049 3461 y(ation)i(at)g(o)r(dd)f(depth) f(b)r(eing)i(far)h(b)r(etter)e(than)g(one)g(at)h(an)g(ev)n(en)2049 3544 y(depth)29 b(b)r(ecause)i(who)r(ev)n(er)g(just)g(mo)n(v)n(ed)e (has)i(just)f(giv)n(en)h(mobilit)n(y)2049 3627 y(to)h(their)f(opp)r (onen)n(t.)51 b(\(Othello)32 b(is)g(a)g(game)f(of)h(zugzw)n(ang.\))53 b(F)-6 b(ur-)2049 3710 y(thermore,)38 b(the)e(Othello)g(program)g(sho)n (ws)g(some)g(v)n(ery)f(unstable)2049 3793 y(principal)24 b(v)l(ariations.)35 b(This)24 b(has)g(the)g(uncommon)d(e\013ect)j(that) f(the)2049 3876 y Fw(\013\014)37 b Fx(searc)n(h)c(is)g(b)r(etter)f (than)g(NegaScout[19)q(,)h(20)q(])g(searc)n(h)g(for)g(this)2049 3960 y(program.)2164 4107 y(In)f(con)n(trast,)k(the)c(c)n(hess)h (program)g(used)f(a)i(fast)f(incremen)n(tal)2049 4190 y(ev)l(aluation)38 b(function)h(based)f(on)g(an)g(Oracle[3)q(])h(com)n (bined)e(with)2049 4273 y(Piece/Color/Square)48 b(tables,)j(and)44 b(pro)r(duced)h(a)g(fairly)h(stable)2049 4356 y(ev)l(aluation)32 b(function)f(and)g(also)h(stable)g(principal)g(v)l(ariations)g(as-)2049 4439 y(so)r(ciated)27 b(with)f(optimised)f(k)n(ey)g(mo)n(v)n(e)f (ordering)j(tec)n(hniques.)2164 4586 y(Whatev)n(er)20 b(the)g(n)n(um)n(b)r(er)e(of)j(pro)r(cessors)h(is,)g(the)d(global)j(n)n (um)n(b)r(er)2049 4669 y(of)k(en)n(tries)g(in)g(the)f(transp)r(osition) i(table)f(is)g(k)n(ept)f(constan)n(t.)2049 4941 y Fy(3.1)100 b(DEFINITIONS)2049 5141 y Fx(Before)35 b(giving)f(some)f(results)g (from)g(the)g(exp)r(erimen)n(ts)f(w)n(e)i(made)2049 5224 y(on)20 b(a)g(CM5)i(Thinking)e(Mac)n(hine)g(Corp)r(oration)i(Computer)d (with)h(32)2049 5307 y(SP)-6 b(AR)n(C)30 b(no)r(des,)j(w)n(e)f(need)f (some)g(basic)h(de\014nitions)f(of)h(the)f(mea-)2049 5390 y(sures)26 b(w)n(e)g(used.)p 2049 5456 801 4 v 2134 5510 a Fv(3)2168 5535 y Fr(The)i(sequen)n(tial)f(Othello)g(program)h (named)f Fk(Bugs)33 b Fr(\014nished)26 b(fourth)i(in)2049 5599 y(the)21 b(W)-5 b(aterlo)r(o)22 b(Othello)f(tournamen)n(t)f(in)i (1994,)h(and)e(\014nished)g(second)g(of)h(the)2049 5663 y(P)n(aderb)r(orn)f(Othello)g(tournamen)n(t)f(in)i(1995.)p eop %%Page: 3 3 3 2 bop -150 540 a Fp(p)n(ro)r(c)p -150 553 128 4 v 25 w(RetrieveAsk)q Fo(\()p Fp(P)n(osition)r Fn(;)11 b(\013;)h(\014)s(;)f Fp(depth)r Fn(;)h Fp(exclusiveP)p Fo(\))44 b Fm(\021)1 615 y Fp(va)n(r)p 1 628 89 4 v 23 w(entry)r Fn(;)11 b Fp(answ)n(er)r Fo(;)43 b Fp(end)p 558 628 105 4 v 1 689 a(entry)21 b Fm( )e(T)f Fo(\()p Fp(P)n(osition)q Fo(\);)1 764 y Fp(answ)n(er)r Fn(:\013)h Fm( )g Fn(\013)p Fo(;)32 b Fp(answ)n(er)r Fn(:\014)22 b Fm( )d Fn(\014)s Fo(;)1 839 y Fp(answ)n(er)r Fn(:)p Fp(sco)n(re)h Fm( )f(\0001)p Fo(;)1 913 y Fp(if)p 1 926 39 4 v 23 w(entry)i Fo(=)f(0)j Fp(then)p 366 926 130 4 v 520 988 a Fo(If)g(not)i(exists)e(then)i(exit) 520 1063 y Fl(skip)e Fp(endp)n(rob)r(e)s Fo(;)1 1138 y Fp(\014)p 1 1151 38 4 v 1 1212 a(if)p 1 1225 39 4 v 23 w(entry)r Fn(:)p Fp(height)e Fo(=)e Fp(depth)34 b Fm(^)d Fp(exclusiveP)h Fm(^)f Fp(entry)r Fn(:)p Fp(np)n(ro)r(c)21 b Fn(>)e Fo(0)63 1287 y Fp(then)p 63 1300 130 4 v 239 1362 a Fo(Only)24 b(one)g(pro)r(cessor)g(allo)n(w)n(ed)g(if)f (exclusivit)n(y)216 1436 y(is)g(required)216 1511 y Fp(answ)n(er)r Fn(:)p Fp(sco)n(re)d Fm( )g Fp(ON)p 799 1511 22 4 v 25 w(EV)-6 b(ALUA)g(TION)q Fo(;)216 1586 y Fl(skip)23 b Fp(endp)n(rob)r(e)1 1661 y(\014)p 1 1674 38 4 v 1 1735 a(if)p 1 1748 39 4 v 23 w(entry)r Fn(:)p Fp(height)e Fm(\025)e Fp(depth)63 1810 y(then)p 63 1823 130 4 v 216 1885 a(if)p 216 1898 39 4 v 23 w(entry)r Fn(:)p Fp(\015ag)h Fo(=)f Fp(V)-6 b(ALID)278 1960 y(then)p 278 1973 130 4 v 25 w(answ)n(er)r Fn(:)p Fp(sco)n(re)21 b Fm( )e Fp(entry)r Fn(:)p Fp(sco)n(re)p Fo(;)431 2034 y Fp(answ)n(er)r Fn(:)p Fp(alpha)h Fm( )f Fp(entry)r Fn(:)p Fp(sco)n(re)q Fo(;)431 2109 y Fp(answ)n(er)r Fn(:\014)j Fm( )e Fp(entry)q Fn(:)p Fp(sco)n(re)216 2184 y(elsif)p 216 2197 114 4 v 23 w(entry)r Fn(:)p Fp(\015ag)g Fo(=)g Fp(UBOUND)32 b Fm(^)f Fp(entry)r Fn(:)p Fp(sco)n(re)20 b Fn(<)g(\014)353 2258 y Fp(then)p 353 2271 130 4 v 25 w(answ)n(er)r Fn(:)p Fp(sco)n(re)h Fm( )e Fp(entry)r Fn(:)p Fp(sco)n(re)q Fo(;)506 2333 y Fp(answ)n(er)r Fn(:\014)k Fm( )c Fp(entry)r Fn(:)p Fp(sco)n(re)216 2408 y(elsif)p 216 2421 114 4 v 23 w(entry)r Fn(:)p Fp(\015ag)h Fo(=)g Fp(LBOUND)32 b Fm(^)f Fp(entry)r Fn(:)p Fp(sco)n(re)20 b Fn(>)g(\013)353 2483 y 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4409 2413 M 252 0 V 1552 686 M 814 -26 V 814 89 V 814 19 V 4493 2413 S 1552 686 S 2366 660 S 3180 749 S 3994 768 S LT6 4325 2273 M (3) Rshow 4409 2273 M 252 0 V 1552 655 M 814 0 V 814 0 V 814 0 V 4493 2273 D 1552 655 D 2366 655 D 3180 655 D 3994 655 D stroke grestore end showpage %%EndDocument @endspecial 37 1948 a @beginspecial 50 @llx 50 @lly 302 @urx 226 @ury 1530 @rwi @setspecial %%BeginDocument: tgraph6.eps /gnudict 40 dict def gnudict begin /Color false def /Solid false def /gnulinewidth 5.000 def /vshift -46 def /dl {10 mul} def /hpt 31.5 def /vpt 31.5 def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop Solid {pop []} if 0 setdash} ifelse } def /BL { stroke gnulinewidth 2 mul setlinewidth } def /AL { stroke gnulinewidth 2 div setlinewidth } def /PL { stroke gnulinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 0 1 0 DL } def /LT1 { PL [4 dl 2 dl] 0 0 1 DL } def /LT2 { PL [2 dl 3 dl] 1 0 0 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /P { stroke [] 0 setdash currentlinewidth 2 div sub M 0 currentlinewidth V stroke } def /D { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke P } def /A { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke P } def /C { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke P } def /S { 2 copy A C} def end gnudict begin gsave 50 50 translate 0.050 0.050 scale 0 setgray /Helvetica findfont 140 scalefont setfont newpath LTa 840 351 M 3968 0 V LTb 840 351 M 63 0 V 3905 0 R -63 0 V 756 351 M (0) Rshow 840 775 M 63 0 V 3905 0 R -63 0 V 756 775 M (20) Rshow 840 1198 M 63 0 V 3905 0 R -63 0 V -3989 0 R (40) Rshow 840 1622 M 63 0 V 3905 0 R -63 0 V -3989 0 R (60) Rshow 840 2045 M 63 0 V 3905 0 R -63 0 V -3989 0 R (80) Rshow 840 2469 M 63 0 V 3905 0 R -63 0 V -3989 0 R (100) Rshow 840 2892 M 63 0 V 3905 0 R -63 0 V -3989 0 R (120) Rshow 840 3316 M 63 0 V 3905 0 R -63 0 V -3989 0 R (140) Rshow 1247 351 M 0 63 V 0 2902 R 0 -63 V 0 -3042 R (5) Cshow 1756 351 M 0 63 V 0 2902 R 0 -63 V 0 -3042 R (10) Cshow 2264 351 M 0 63 V 0 2902 R 0 -63 V 0 -3042 R (15) Cshow 2773 351 M 0 63 V 0 2902 R 0 -63 V 0 -3042 R (20) Cshow 3282 351 M 0 63 V 0 2902 R 0 -63 V 0 -3042 R (25) Cshow 3791 351 M 0 63 V 0 2902 R 0 -63 V 0 -3042 R (30) Cshow 4299 351 M 0 63 V 0 2902 R 0 -63 V 0 -3042 R (35) Cshow 4808 351 M 0 63 V 0 2902 R 0 -63 V 0 -3042 R (40) Cshow 840 351 M 3968 0 V 0 2965 V -3968 0 V 840 351 L 140 1833 M currentpoint gsave translate 90 rotate 0 0 M (Overheads) Cshow grestore 2824 71 M (Number of processors) Cshow 2824 3456 M (Othello : ABDADA) Cshow LT0 4325 3113 M ( TO) Rshow 4409 3113 M 252 0 V -667 80 R 3180 2249 L 2366 1391 L 1552 672 L 4493 3113 D 3994 3193 D 3180 2249 D 2366 1391 D 1552 672 D LT1 4325 2973 M ( SO) Rshow 4409 2973 M 252 0 V 3994 2271 M 3180 1619 L 2366 1016 L 1552 460 L 4493 2973 A 3994 2271 A 3180 1619 A 2366 1016 A 1552 460 A LT2 4325 2833 M ( CO) Rshow 4409 2833 M 252 0 V 3994 1273 M 3180 981 L 2366 726 L 1552 563 L 4493 2833 B 3994 1273 B 3180 981 B 2366 726 B 1552 563 B LT3 4325 2693 M ( SY) Rshow 4409 2693 M 252 0 V 3994 351 M -814 0 V -814 0 V -814 0 V 4493 2693 C 3994 351 C 3180 351 C 2366 351 C 1552 351 C stroke grestore end showpage %%EndDocument @endspecial 1275 w @beginspecial 50 @llx 50 @lly 302 @urx 226 @ury 1530 @rwi @setspecial %%BeginDocument: tgraph24.eps /gnudict 40 dict def gnudict begin /Color false def /Solid false def /gnulinewidth 5.000 def /vshift -46 def /dl {10 mul} def /hpt 31.5 def /vpt 31.5 def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop Solid {pop []} if 0 setdash} ifelse } def /BL { stroke gnulinewidth 2 mul setlinewidth } def /AL { stroke gnulinewidth 2 div setlinewidth } def /PL { stroke gnulinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 0 1 0 DL } def /LT1 { PL [4 dl 2 dl] 0 0 1 DL } def /LT2 { PL [2 dl 3 dl] 1 0 0 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /P { stroke [] 0 setdash currentlinewidth 2 div sub M 0 currentlinewidth V stroke } def /D { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke P } def /A { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke P } def /C { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke P } def /S { 2 copy A C} def end gnudict begin gsave 50 50 translate 0.050 0.050 scale 0 setgray /Helvetica findfont 140 scalefont setfont newpath LTa 840 351 M 3968 0 V LTb 840 351 M 63 0 V 3905 0 R -63 0 V 756 351 M (0) Rshow 840 722 M 63 0 V 3905 0 R -63 0 V 756 722 M (10) Rshow 840 1092 M 63 0 V 3905 0 R -63 0 V -3989 0 R (20) Rshow 840 1463 M 63 0 V 3905 0 R -63 0 V -3989 0 R (30) Rshow 840 1834 M 63 0 V 3905 0 R -63 0 V -3989 0 R (40) Rshow 840 2204 M 63 0 V 3905 0 R -63 0 V -3989 0 R (50) Rshow 840 2575 M 63 0 V 3905 0 R -63 0 V -3989 0 R (60) Rshow 840 2945 M 63 0 V 3905 0 R -63 0 V -3989 0 R (70) Rshow 840 3316 M 63 0 V 3905 0 R -63 0 V 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2833 M 252 0 V 1552 643 M 814 57 V 814 64 V 814 37 V 4493 2833 B 1552 643 B 2366 700 B 3180 764 B 3994 801 B LT3 4325 2693 M (SY) Rshow 4409 2693 M 252 0 V 1552 351 M 814 0 V 814 0 V 814 0 V 4493 2693 C 1552 351 C 2366 351 C 3180 351 C 3994 351 C stroke grestore end showpage %%EndDocument @endspecial 1276 w @beginspecial 50 @llx 50 @lly 302 @urx 226 @ury 1530 @rwi @setspecial %%BeginDocument: tgraph28.eps /gnudict 40 dict def gnudict begin /Color false def /Solid false def /gnulinewidth 5.000 def /vshift -46 def /dl {10 mul} def /hpt 31.5 def /vpt 31.5 def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop Solid {pop []} if 0 setdash} ifelse } def /BL { stroke gnulinewidth 2 mul setlinewidth } def /AL { stroke gnulinewidth 2 div setlinewidth } def /PL { stroke gnulinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 0 1 0 DL } def /LT1 { PL [4 dl 2 dl] 0 0 1 DL } def /LT2 { PL [2 dl 3 dl] 1 0 0 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /P { stroke [] 0 setdash currentlinewidth 2 div sub M 0 currentlinewidth V stroke } def /D { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke P } def /A { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /B { stroke [] 0 setdash 2 copy 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0.00 0.00 0.00 1.00 k e /_AvantGarde-Book 200.00 z 0 0 (ABDADA 32) @t T @rs @rs end %%EndDocument @endspecial 166 x(Figure)20 b(5:)32 b(Comparison)20 b(of)g(absolute)g(sp)r(eedups)f(for)h(b)r(oth)f(sc)n(hemes)-150 4625 y(applied)26 b(to)g(Othello)g(for)g(8,)h(16,)f(24,)h(32)f(pro)r (cessors)-35 4808 y(Figure)k(5)g(sho)n(ws)h(the)e(comparison)h(of)g(sp) r(eed)g(on)f(the)h(Othello)-150 4891 y(program)20 b(compared)g(to)g (the)g(fastest)h(sequen)n(tial)f(Othello)h(program)-150 4974 y(w)n(e)35 b(ha)n(v)n(e,)j(the)c(recursiv)n(e)h Fw(\013\014)t Fx(.)63 b(W)-6 b(e)35 b(can)g(see)h(that)e(up)h(to)g (depth)-150 5057 y(8,)e(ABD)n(AD)n(A)c(is)j(more)e(e\016cien)n(t)h (than)g(YBW)n(C)g(searc)n(h)h(but)e(this)-150 5140 y(c)n(hanges)c(in)g (depths)f(greater)h(than)g(9.)p -150 5200 801 4 v -150 5267 a Fr(there)21 b(is)h(no)g(go)r(o)r(d)g(c)n(hoice)e(and)i(w)n(e)g (did)f(it)h(in)g(order)f(to)h(ha)n(v)n(e)g(results)g(compa-)-150 5330 y(rable)f(with)i(those)e(from)h(previous)f(publications.)-65 5382 y Fv(9)-31 5407 y Fr(In)k(the)e(pseudo)h(co)r(de)f(giv)n(en)h(in)h (part)f(2)h(the)f(eldest)f(no)r(de)h(is)h(read)f(t)n(wice)-150 5471 y(and)d(so)h(are)f(all)g(no)r(des)f(ev)l(aluated)h(in)g(the)f (second)g(pass.)30 b(This)21 b(is)h(the)f(v)n(ersion)-150 5535 y(w)n(e)h(used)e(in)h(our)g(exp)r(erimen)n(ts)e(for)i(simplicit)n (y)e(of)i(co)r(de)f(but)h(it)g(is)h(really)e(easy)-150 5599 y(to)27 b(impro)n(v)n(e)e(the)g(searc)n(h)h(b)n(y)g(searc)n(hing)g (only)g(the)f(non-ev)l(aluated)g(no)r(des)h(in)-150 5662 y(the)c(third)f(pass.)2049 3280 y @beginspecial 48 @llx 299 @lly 542 @urx 570 @ury 1984 @rwi @setspecial %%BeginDocument: chess.eps /AutoFlatness false def % -------------- POSTSCRIPT PROLOG FOR CORELDRAW 3.X ------ % Copyright 1992 Corel Corporation. 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16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/oe 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis ] def/@cc{currentfile $dat readhexstring pop}bd /@sm{/$ctm $ctm currentmatrix def}bd/@E{/Bbury xd/Bburx xd /Bblly xd/Bbllx xd}bd/@c{@cp}bd/@p{/$fil 1 def 1 eq/$vectpat xd/$pm xd/$psy xd/$psx xd/$pyf xd/$pxf xd /$pn xd}bd/@P{/$fil 3 def/$Psn xd array astore /$Prm xd}bd/@k{/$fil 2 def/$roy xd/$rox xd/$pad xd /$fty xd/$fan xd $fty 1 eq{/$fan 0 def}if/$tok xd/$toy xd/$tom xd/$toc xd /$frk xd/$fry xd/$frm xd/$frc xd/$frn _ def/$frt 1 def/$ton _ def/$tot 1 def }bd/@x{/$fil 2 def/$roy xd/$rox xd/$pad xd /$fty xd/$fan xd/$tot xd/$ton xd/$tok xd/$toy xd/$tom xd/$toc xd /$frt xd/$frn xd/$frk xd/$fry xd/$frm xd/$frc xd}bd /@ii{concat 3 index 3 index m 3 index 1 index l 2 copy l 1 index 3 index l 3 index 3 index l clip pop pop pop pop}bd/@i{@sm @gs @ii 6 index 1 ne{/$frg true def pop pop}{1 eq{$T $C $M $Y $K $N $O @scc/$frg xd}{/$frg false def }ifelse 1 eq{@gs $ctm setmatrix $t $c $m $y $k $n $o @scc{eofill}if @gr}if}ifelse/$frg $frg $bkg or def @np/$ury xd/$urx xd/$lly xd/$llx xd /$bts xd/$hei xd/$wid xd/$dat $wid $bts mul 8 div ceiling cvi string def $frg{$SDF{$SCF $SCA $SCP @ss}if $llx $lly translate $urx $llx sub $ury $lly sub scale $wid $hei abs $bts 1 eq{false}{$bts}ifelse [ $wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/@cc load $bts 1 eq{imagemask}{image}ifelse $SDF{$dsf $dsa $dsp @ss}if}{$hei abs{@cc pop}repeat}ifelse @gr $ctm setmatrix}def/@M{@sv}bd/@N{/@cc{}def 1 eq{12 -1 roll neg 12 1 roll @I}{13 -1 roll neg 13 1 roll @i}ifelse @rs}bd/@I{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd/$llx xd /$ncl xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $llx $lly translate $urx $llx sub $ury $lly sub scale $wid $hei abs $bts [ $wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse] /@cc load false $ncl colorimage @gr $ctm setmatrix}bd /z{exch findfont exch scalefont setfont}bd /ZB{9 dict dup begin 4 1 roll/FontType 3 def /FontMatrix xd/FontBBox xd/Encoding 256 array def 0 1 255{Encoding exch/.notdef put}for/CharStrings 256 dict def CharStrings/.notdef{}put/Metrics 256 dict def Metrics/.notdef 3 -1 roll put/BuildChar{exch dup/$char exch/Encoding get 3 index get def dup/Metrics get $char get aload pop setcachedevice begin Encoding exch get CharStrings exch get end exec}def end definefont pop}bd/ZBAddChar{findfont begin dup 4 1 roll dup 6 1 roll Encoding 3 1 roll put CharStrings 3 1 roll put Metrics 3 1 roll put end}bd/Z{findfont dup maxlength 2 add dict exch dup{1 index/FID ne{3 index 3 1 roll put}{pop pop}ifelse}forall pop dup dup/Encoding get 256 array copy dup/$fe xd /Encoding exch put dup/Fontname 3 index put 3 -1 roll dup length 0 ne{0 exch{dup type 0 type eq{exch pop}{ $fe exch 2 index exch put 1 add}ifelse}forall pop}if dup 256 dict dup/$met xd/Metrics exch put dup/FontMatrix get 0 get 1000 mul 1 exch div 3 index length 256 eq{0 1 255{dup $fe exch get dup/.notdef eq{pop pop}{5 index 3 -1 roll get 2 index mul $met 3 1 roll put}ifelse}for}if pop definefont pop pop}bd/@ftx{{(0) dup 3 -1 roll 0 exch put @gs true charpath $ctm setmatrix @@txt @gr @np}forall}bd /@ft{matrix currentmatrix exch $sdf{$scf $sca $scp @ss}if $fil 1 eq{/@@txt/@pf ld @ftx}{$fil 2 eq{/@@txt/@ff ld @ftx}{$fil 3 eq {/@@txt/@Pf ld @ftx}{$t $c $m $y $k $n $o @scc{show}{pop}ifelse}ifelse }ifelse}ifelse $sdf{$dsf $dsa $dsp @ss}if setmatrix}bd /@st{matrix currentmatrix exch $SDF{$SCF $SCA $SCP @ss}if $T $C $M $Y $K $N $O @scc{{(0) dup 3 -1 roll 0 exch put @gs true charpath $ctm setmatrix $ptm concat stroke @gr}forall}{pop}ifelse $SDF{$dsf $dsa $dsp @ss}if setmatrix}bd/@te{@ft}bd/@tr{@st}bd/@ta{dup @gs @ft @gr @st}bd/@t@a{dup @gs @st @gr @ft}bd /@tm{/$textsave save def @sm concat}bd/e{/t{@te}def}bd /r{/t{@tr}def}bd/o{/t{pop}def}bd/a{/t{@ta}def}bd /@a{/t{@t@a}def}bd/t{@te}def/T{@np $ctm setmatrix /$ttm matrix def $textsave restore}bd/@t{/$stm $stm currentmatrix def 3 1 roll moveto $ttm concat t $stm setmatrix}def /@n{/$ttm exch matrix rotate def}bd/@s{}bd /@l{}bd/@B{@gs S @gr F}bd/@b{@cp @B}bd/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix/$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd{/$scp xd/$sca xd /$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd /$SCA xd/$SCF xd}if}bd/@D{3 copy @ss/$dsp xd /$dsa xd/$dsf xd}bd/@j{@sv @np}bind def/@J{@rs}bind def /@sep{/ColorSeparationMode where{pop}{/ColorSeparationMode 0 def /CurrentInkName (Composite) def}ifelse ColorSeparationMode 0 eq{ /CurrentInkName (Composite) def}if/CurrentInkName where{pop}{ /CurrentInkName (Composite) def}ifelse CurrentInkName (Composite) eq {/$ink -1 def}{CurrentInkName (Cyan) eq{/$ink 0 def}{ CurrentInkName (Magenta) eq{/$ink 1 def}{CurrentInkName (Yellow) eq {/$ink 2 def}{CurrentInkName (Black) eq{/$ink 3 def}{/$ink 4 def }ifelse}ifelse}ifelse}ifelse}ifelse}bd @sep /@whi{@gs -72000 dup moveto -72000 72000 lineto 72000 dup lineto 72000 -72000 lineto closepath 1 setgray fill @gr}bd/@neg{ [{1 exch sub}/exec cvx currenttransfer/exec cvx] cvx settransfer @whi}bd/@reg{[] 0 d 0 setgray .3 setlinewidth 2 copy 5.4 0 360 arc closepath 2 copy moveto 9 0 rlineto 2 copy moveto -9 0 rlineto 2 copy moveto 0 9 rlineto moveto 0 -9 rlineto stroke}bd/leftbracket{(\050)}def /rightbracket{(\051)}def 11.4737 setmiterlimit 1.00 setflat /$fst 128 def @sv /$ctm matrix currentmatrix def @sv 71.21 354.67 469.58 354.96 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 71.21 354.82 m 469.58 354.82 L S 71.21 382.25 469.58 382.54 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 71.21 382.39 m 469.58 382.39 L S 71.21 409.75 469.58 410.04 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 71.21 409.90 m 469.58 409.90 L S 71.21 437.33 469.58 437.62 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 71.21 437.47 m 469.58 437.47 L S 71.21 464.83 469.58 465.12 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 71.21 464.98 m 469.58 464.98 L S 71.21 492.34 469.58 492.62 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 71.21 492.48 m 469.58 492.48 L S 71.21 519.91 469.58 520.20 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 71.21 520.06 m 469.58 520.06 L S 71.21 547.42 469.58 547.70 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 71.21 547.56 m 469.58 547.56 L S 73.15 327.31 81.00 342.58 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 73.15 342.58 m 81.00 342.58 L 81.00 327.31 L 73.15 327.31 L 73.15 342.58 L @c B 139.54 327.31 147.38 357.05 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 139.54 357.05 m 147.38 357.05 L 147.38 327.31 L 139.54 327.31 L 139.54 357.05 L @c B 205.99 327.31 213.77 362.95 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 205.99 362.95 m 213.77 362.95 L 213.77 327.31 L 205.99 327.31 L 205.99 362.95 L @c B 272.38 327.31 280.22 377.42 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 272.38 377.42 m 280.22 377.42 L 280.22 327.31 L 272.38 327.31 L 272.38 377.42 L @c B 338.76 327.31 346.54 382.39 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 338.76 382.39 m 346.54 382.39 L 346.54 327.31 L 338.76 327.31 L 338.76 382.39 L @c B 405.14 327.31 412.92 388.01 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 405.14 388.01 m 412.92 388.01 L 412.92 327.31 L 405.14 327.31 L 405.14 388.01 L @c B 81.00 327.31 88.78 396.14 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 2.16 2.16 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 81.00 396.14 m 88.78 396.14 L 88.78 327.31 L 81.00 327.31 L 81.00 396.14 L @c B 147.38 327.31 155.23 401.62 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 2.16 2.16 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 147.38 401.62 m 155.23 401.62 L 155.23 327.31 L 147.38 327.31 L 147.38 401.62 L @c B 213.77 327.31 221.62 395.86 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 2.16 2.16 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 213.77 395.86 m 221.62 395.86 L 221.62 327.31 L 213.77 327.31 L 213.77 395.86 L @c B 280.22 327.31 288.00 389.66 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 2.16 2.16 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 280.22 389.66 m 288.00 389.66 L 288.00 327.31 L 280.22 327.31 L 280.22 389.66 L @c B 346.54 327.31 354.38 401.26 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 2.16 2.16 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 346.54 401.26 m 354.38 401.26 L 354.38 327.31 L 346.54 327.31 L 346.54 401.26 L @c B 412.92 327.31 420.77 408.53 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 2.16 2.16 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.00 k 412.92 408.53 m 420.77 408.53 L 420.77 327.31 L 412.92 327.31 L 412.92 408.53 L @c B 88.78 327.31 96.62 350.28 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.74 k 88.78 350.28 m 96.62 350.28 L 96.62 327.31 L 88.78 327.31 L 88.78 350.28 L @c B 155.23 327.31 163.01 363.89 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.74 k 155.23 363.89 m 163.01 363.89 L 163.01 327.31 L 155.23 327.31 L 155.23 363.89 L @c B 221.62 327.31 229.39 370.51 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.74 k 221.62 370.51 m 229.39 370.51 L 229.39 327.31 L 221.62 327.31 L 221.62 370.51 L @c B 288.00 327.31 295.85 397.87 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.74 k 288.00 397.87 m 295.85 397.87 L 295.85 327.31 L 288.00 327.31 L 288.00 397.87 L @c B 354.38 327.31 362.16 410.98 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.74 k 354.38 410.98 m 362.16 410.98 L 362.16 327.31 L 354.38 327.31 L 354.38 410.98 L @c B 420.77 327.31 428.62 431.21 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.74 k 420.77 431.21 m 428.62 431.21 L 428.62 327.31 L 420.77 327.31 L 420.77 431.21 L @c B 96.62 327.31 104.40 396.14 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 2.16 2.16 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.74 k 96.62 396.14 m 104.40 396.14 L 104.40 327.31 L 96.62 327.31 L 96.62 396.14 L @c B 163.01 327.31 170.86 396.94 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 2.16 2.16 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.74 k 163.01 396.94 m 170.86 396.94 L 170.86 327.31 L 163.01 327.31 L 163.01 396.94 L @c B 229.39 327.31 237.24 406.15 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 2.16 2.16 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.74 k 229.39 406.15 m 237.24 406.15 L 237.24 327.31 L 229.39 327.31 L 229.39 406.15 L @c B 295.85 327.31 303.62 423.58 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 2.16 2.16 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.74 k 295.85 423.58 m 303.62 423.58 L 303.62 327.31 L 295.85 327.31 L 295.85 423.58 L @c B 362.16 327.31 370.01 442.44 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 2.16 2.16 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.74 k 362.16 442.44 m 370.01 442.44 L 370.01 327.31 L 362.16 327.31 L 362.16 442.44 L @c B 428.62 327.31 436.39 464.83 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 2.16 2.16 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.74 k 428.62 464.83 m 436.39 464.83 L 436.39 327.31 L 428.62 327.31 L 428.62 464.83 L @c B 104.40 327.31 112.25 350.28 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.49 k 104.40 350.28 m 112.25 350.28 L 112.25 327.31 L 104.40 327.31 L 104.40 350.28 L @c B 170.86 327.31 178.63 363.89 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.49 k 170.86 363.89 m 178.63 363.89 L 178.63 327.31 L 170.86 327.31 L 170.86 363.89 L @c B 237.24 327.31 245.09 379.08 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.49 k 237.24 379.08 m 245.09 379.08 L 245.09 327.31 L 237.24 327.31 L 237.24 379.08 L @c B 303.62 327.31 311.47 416.74 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.49 k 303.62 416.74 m 311.47 416.74 L 311.47 327.31 L 303.62 327.31 L 303.62 416.74 L @c B 370.01 327.31 377.78 438.98 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.49 k 370.01 438.98 m 377.78 438.98 L 377.78 327.31 L 370.01 327.31 L 370.01 438.98 L @c B 436.39 327.31 444.24 469.08 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 0.07 0.07 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.49 k 436.39 469.08 m 444.24 469.08 L 444.24 327.31 L 436.39 327.31 L 436.39 469.08 L @c B 112.25 327.31 120.10 396.14 @E 0 J 0 j [] 0 d 0 R 0 @G 0.00 0.00 0.00 1.00 K [0.63127 0.00000 0.00000 0.63127 0 0] 1 2.16 2.16 0.00 @w 0 O 0 @g 0.00 0.00 0.00 0.49 k 112.25 396.14 m 120.10 396.14 L 120.10 327.31 L 112.25 327.31 L 112.25 396.14 L @c B 178.63 327.31 186.48 413.06 @E 0 J 0 j [] 0 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b(in)h(editing)g(the)f(do)r(cumen)n(t.)2164 5017 y(Thanks)44 b(also)i(to)f(m)n(y)d(thesis)j(review)n(ers,)51 b(T)-6 b(on)n(y)44 b(Marsland,)2049 5100 y(Jacques)33 b(Pitrat)g(and)g(Mic)n (hel)g(Gondran)g(for)g(all)h(their)e(construc-)2049 5183 y(tiv)n(e)25 b(criticism)h(on)g(Chapter)g(4)g(of)g(m)n(y)e(thesis.)2164 5330 y(The)k(presen)n(t)f(w)n(ork)g(has)h(b)r(een)f(p)r(erformed)g(in)g (the)g(framew)n(ork)2049 5413 y(of)f(the)f Fs(F)-6 b(r)l(enchess)34 b Fx(pro)t(ject,)26 b(part)f(of)h(a)g(join)n(t)f(researc)n(h)h (e\013ort)g(with)2049 5496 y(Electricit)n(\023)-36 b(e)28 b(de)f(F)-6 b(rance)27 b(\(departmen)n(t)e(EDF/DER/TIEM/IMA\))2049 5579 y(and)35 b(the)f(Arti\014cial)i(In)n(telligence)g(Institut)e(of)i (the)f(univ)n(ersit)n(y)f(of)2049 5662 y(P)n(aris)27 b(8.)p eop %%Page: 8 8 8 7 bop -150 83 a Fy(REFERENCES)-112 254 y Fx([1])40 b Fa(Barriuso,)29 b(R.,)h(and)f(Knies,)g(A.)38 b Fs(SHMEM)28 b(User's)h(Guide)8 337 y(R)l(evision)f(1.08)p Fx(.)34 b(CRA)-6 b(Y)25 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Fx(Chess)27 b(on)g(a)h(h)n(yp)r(ercub)r(e.)37 b(In)8 5579 y Fs(The)30 b(Thir)l(d)g(Confer)l(enc)l(e)h(on)f(Hyp)l(er)l (cub)l(e)i(Concurr)l(ent)g(Com-)8 5663 y(puters)d(and)f(Applic)l (ations)33 b Fx(\(1988\),)27 b(v)n(ol.)f(2,)g(pp.)g(1329{1341.)2049 83 y([19])40 b Fa(Pearl,)26 b(J.)j Fx(Asymptotic)21 b(prop)r(erties)i (of)g(minimax)d(trees)j(and)2207 166 y(game-searc)n(hing)40 b(pro)r(cedures.)75 b Fs(A)n(rti\014cial)40 b(Intel)t(ligenc)l(e)h(14) 2207 249 y Fx(\(1980\),)27 b(113{138.)2049 365 y([20])40 b Fa(Reinefeld,)k(A.)74 b Fx(An)39 b(impro)n(v)n(emen)n(t)d(to)k(the)f (scout)g(tree-)2207 448 y(searc)n(h)26 b(algorithm.)35 b Fs(ICCA)27 b(Journal)h(6)p Fx(,)e(4)g(\(1983\),)h(4{14.)2049 565 y([21])40 b Fa(Schaeffer,)30 b(J.)40 b Fx(Distributed)27 b(game-tree)h(searc)n(h.)41 b Fs(Journal)2207 648 y(of)28 b(Par)l(al)t(lel)g(and)h(Distribute)l(d)h(Computing)f(6)p Fx(,)e(2)g(\(1989\),)i(90{)2207 731 y(114.)2049 847 y([22])40 b Fa(Thinking)f(Ma)n(chines)h(Corpora)-5 b(tion)p Fx(.)71 b 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