Disjoint Pattern Database Heuristics
Disjoint Pattern Database Heuristics
Disjoint Pattern Database Heuristics
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onedatabase.Thereasonisthateverytwistofthecubemovesfouredge cubiesandfourcornercubies,andmovesthatcontributetothesolutionof cubiesinonepatterndatabasemayalsocontributetothesolutionofthe cost,istotaketheirmaximum,eventhougheachcubiebelongstoonly<br />
Rubik'sCube[10].Themedianoptimalsolutionlengthisonly18moves. Oneprobleminstancegeneratedatrillionnodes,andrequiredacoupleweeks valuesdescribedabove,willndoptimalsolutionstorandominstancesof others.IDA*,usingthemaximumofthethreepattern-databaseheuristic<br />
torun.WithimprovementsbyMichaelReidandHerbertKociemba,larger patterndatabases,andfastercomputers,moststatescannowbesolved optimallyinaboutanhour. 2.2.2LimitationsofNon-Additive<strong>Pattern</strong><strong>Database</strong>s<br />
25!=(25n1)!entries.Adatabaseofonlysixtilesandtheblankwould solvelargerproblems.Forexample,sincetheTwenty-Fourpuzzlecontains25 dierentpositions,apatterndatabasecoveringntilesandtheblankrequires Themainlimitationofnon-additivepatterndatabasesisthattheycan't<br />
takethemaximumoftheirvalues,evenifthesetsoftilesaredisjoint.The Withmultipledatabases,thebestwaytocombinethemadmissiblyisto onlysixtileswouldbesmallerthantheManhattandistanceofallthetiles. requireover2.2billionentries.Furthermore,thevaluesfromadatabaseof<br />
reasonisthatnon-additivepatterndatabasevaluesincludeallmovesneeded tosolvethepatterntiles,includingmovesofothertiles. wouldliketobeabletosumtheirvalues,togetamoreaccurateheuristic, withoutviolatingadmissibility.Thisisthemainideaofdisjointpattern databases. Insteadoftakingthemaximumofdierentpatterndatabasevalues,we<br />
3Toconstructadisjointpatterndatabaseforthesliding-tilepuzzles,wepar-<br />
titionthetilesintodisjointgroups,suchthatnotilebelongstomorethan <strong>Disjoint</strong><strong>Pattern</strong><strong>Database</strong>s<br />
ofthetilesineachgroupthatarerequiredtogetthosetilestotheirgoal onegroup.Wethenprecomputetablesoftheminimumnumberofmoves positions.Wecallthesetofsuchtables,onepergroupoftiles,adisjoint 8
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