Disjoint Pattern Database Heuristics
Disjoint Pattern Database Heuristics
Disjoint Pattern Database Heuristics
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HeuristicFunction ManhattanDistance36.940401,189,630 LinearConicts <strong>Disjoint</strong><strong>Database</strong> Value Nodes Nodes/secSecondsAllSolutions<br />
<strong>Disjoint</strong>+Reected 38.788 44.752 40,224,625 136,289 7,269,026 4,142,193 2,174,362 55.1921,178,106,819 9.710 .063 144,965,491<br />
Table1:ExperimentalResultsontheFifteenPuzzle 45.630 36,710 1,377,630 .027 472,595 130,367<br />
intheorder(12).Toreversethem,oneofthetilesmustmoveoutofthe<br />
ofthesetwotileswithoutviolatingadmissibility.Thesameideacanbeappliedtotilesintheirgoalcolumnaswell.Infact,atileinitsgoalposition<br />
row.SincethesetwomovesarenotcountedintheManhattandistanceof eithertile,twomovescanbeaddedtothesumoftheManhattandistances toprow,toallowtheothertiletopassby,andthenmovebackintothetop<br />
ofmovescanbeaddedtotheManhattandistance,withoutviolatingadmissibility.Thelinear-conictheuristicreducesthenumberofnodesgenerated<br />
thoserequiredtoresolveacolumnconictarehorizontalmoves,bothsets theextramovesrequiredtoresolvearowconictareverticalmoves,and mayparticipateinbotharowandacolumnconictsimultaneously.Since<br />
byanorderofmagnitude,atacostofalmostfactoroftwoinspeed,foran overallspeedupofoverafactorofve,comparedtoManhattandistance.<br />
entryforeciency,occupyingatotalof550megabytes,butthesedatabases databasevaluesdepictedontheleftsideofFigure4.Weusedonebyteper rowrepresentstheheuristicwhichisthesumofthesevenandeight-tile Thenexttworowsarefordisjointpatterndatabaseheuristics.Thethird<br />
putetheManhattandistancesduringthesearch.Furthermore,sincethe exceedingtheManhattandistancesofthepatterntiles,andseparatelycom-<br />
parityoftheadditionalmovesisthesameasthatoftheManhattandistance,wecouldstoreonlyhalfthenumberofadditionalmoves,andmultiply<br />
heuristicofthethirdrow.Wethencomputethesumofthesevenand bytwo. eight-tiledatabasevaluesshownontherightsideofFigure4.Finally,the overallheuristicisthemaximumofthesetwosums.Sincethetwodierent Thefourthrowrepresentsaheuristiccomputedbystartingwiththe<br />
couldbecompressed.Forexample,wecouldstoreonlytheadditionalmoves<br />
bothdatabases,andsimplyreectthetilesandtheirpositionsaboutthe partitionsarereectionsofoneanother,weusethesamepairoftablesfor 11
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