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ONE,TWOANDTHREETIMESlogn=nFORPATHSINA COMPLETEGRAPHWITHRANDOMWEIGHTS Abstract.Considertheminimalweightsofpathsbetweentwopointsin acompletegraphKnwithrandomweightsontheedges,theweightsbeing SVANTEJANSON

By Kn. (thustji=tij. Wedonotdenetijfori=j. )weassumethatthe Letar, Omweighttijbeassignedtoeveryedgeijofthecompletegraph Introduction and Ii)foranyxedi Logn=np! Xij

Abstract

fortwogivenpoints,thatthemaximumifonepointisxedandtheother e.g.uniformlydistributed.Itisshownthat,asymptotically,thisislogn=n variesis2logn=n,andthatthemaximumoverallpairsofpointsis3logn=n. toticdistributionsandmoments,andonthenumberofedgesintheminimal weightpaths. Somefurtherrelatedresultsaregiventoo,includingresultsonasymp

Topics: betweeniandj.Ourmaintheoremisasetofthreedierentasymptotic resultsforXij.(logdenotesthenaturallogarit, fortwoverticesiandj, Xijbetheminimaltotalweightofapath
Year: 2012
OAI identifier: oai:CiteSeerX.psu:10.1.1.228.7114
Provided by: CiteSeerX
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