Disjoint Pattern Database Heuristics
Disjoint Pattern Database Heuristics
Disjoint Pattern Database Heuristics
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duplicatepruning.Therstcolumngivesthecorrespondingproblemnumber in[9],whichwealsosolvedusingthesameheuristicasin[9],butwithout fromTable3,thesecondthelengthoftheoptimalsolution,thethirdthe Table2showscomparativeresultsfortheveeasiestproblemssolved<br />
numberofnodegenerationsfrom[9]withFSMpruning,thefourthcolumn<br />
of[9]generatesabout3;207;000nodespersecondwithoutFSMpruning, pruning,andthefthcolumngivesthenumberofnodesgeneratedwith ourdisjointpatterndatabaseheuristicwithoutFSMpruning.Theprogram thenumberofnodesgeneratedusingthesameheuristicbutwithoutFSM<br />
programonthesamemachine.Takingthisspeeddierenceintoaccount, comparedtoabout2;110;000nodespersecondforourdisjointdatabase<br />
[9],theymaysignicantlyunderestimatetheaveragespeedup.Ontheother Sincethesecomparisonsarebasedontheeasiestproblemsfortheprogramof withoutFSMpruning,whichrangesfromafactorof1.2toafactorof21.8. thelastcolumngivesthespeedupfactorofourprogramoverthatin[9],<br />
itrunsfaster,sinceithasmuchbettercacheperformance. hand,theprogramof[9]usesverylittlememory,whichisthemainreason<br />
Themaindrawbackofdisjointdatabaseheuristicsisthattheydon'tcapture interactionsbetweentilesindierentgroupsofthepartition.Thisrequiresa 5 PairwiseandHigher-OrderDistances<br />
requiredofbothtilestomovethemtotheirgoalpositions.Gasserrefers andeachpossiblepairofpositionstheycouldoccupy,thenumberofmoves sideratableforasliding-tilepuzzlewhichcontainsforeachpairoftiles, dierentapproach,developedindependentlybyGasser[4]andKorf[9].Con-<br />
somepositionshowever,suchastwotilesinalinearconict,theirpairwise pairwisedistances.Formostpairsoftilesinmostpositions,theirpairwise distancewillequalthesumoftheirManhattandistances.Forsometilesin tothistableasthe2-tilepatterndatabase,whilewecallthesevaluesthe<br />
distancewillexceedthesumoftheirManhattandistances.Givenntiles, wisedistancesthatexceedthesumoftheManhattandistancesofthetwo thereareO(n4)entriesinthecomplete2-tiledatabase,butonlythosepair-<br />
thedatabasevaluesforeachpairoftilestocomputetheheuristic,sinceeach tilesneedbestored.Thistableisonlycomputedonceforagivengoalstate. Givena2-tiledatabase,andastateofthepuzzle,wecan'tsimplysum<br />
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