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历史图上基于CSR结构的PageRank算法.docx

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历史图上基于CSR结构的PageRank算法 Abstract PageRankalgorithmisoneofthemostfamousalgorithmsusedbysearchenginestorankwebpages.Thealgorithmworksbyassigningascoretoeachpagebasedonthenumberandqualityoflinkspointingtoit.Inthispaper,wewilldiscussthePageRankalgorithmbasedontheCSRstructureanditshistory.TheCSRstructureisapopulardatastructureusedintheimplementationofsparsematrices.WewillexploretheadvantagesofusingthisstructuretoimprovetheperformanceofthePageRankalgorithm. Introduction PageRankisanalgorithmusedbysearchenginestorankwebpagesbasedontheirimportance.ThealgorithmisnamedafterLarryPage,theco-founderofGoogle,whodevelopeditin1996.Theoriginalalgorithmusedasimplecountingalgorithmtorankpagesbasedonthenumberoflinkspointingtothem.However,thisalgorithmwassoonfoundtobeflawed,asitdidnottakeintoaccountthequalityofthelinks. Toaddressthisissue,thePageRankalgorithmwasdeveloped.Itworksbyassigningascoretoeachpagebasedonthenumberandqualityoflinkspointingtoit.Thealgorithmusesacomplexmathematicalformulatocalculatethescoreofeachpage.ThealgorithmhasbeenadoptedbyothersearchenginesinadditiontoGoogle,suchasYahooandBing. PageRankAlgorithm ThePageRankalgorithmisbasedontheconceptofrandomwalksonthewebgraph.Thewebgraphisagraphthatrepresentstheconnectivityofwebpages.Eachwebpageisrepresentedasanodeinthegraph,andeachlinkbetweenthepagesisrepresentedasanedge.Thealgorithmassumesthatauserrandomlyclickslinksonwebpagesandfollowsthem,withaprobabilityof85%offollowingalinkandaprobabilityof15%ofjumpingtoarandompage. Thealgorithmworksbyassigninganinitialscoreof1/Ntoeachpage,whereNisthetotalnumberofpages.Thealgorithmtheniterativelyupdatesthescoresofthepagesbasedonthescoreofthepageslinkingtoit.Thescoreofapageisdeterminedbythesumofthescoresofthepageslinkingtoit,multipliedbyadampingfactorof0.85. Thealgorithmcontinuestoupdatethescoresuntilconvergenceisreached.Theconvergenceisachievedwhenthescoresofthepagesnolongerchangesignificantly.Atthispoint,thepagesaresortedbytheirscores,andthehighestscoringpagesarereturnedasthetopsearchre