MaximumFlowProblemNotionsanddefinitionsFordandFulkerson’works……worksDefinition:workG=(V,E)isadirectedgraphtogetherwithanonnegativemapC:ER,calledcapacity,andtwodistinguishedverticessandtcalledthesource(withnoin-edges)andthesink(withnoout-edges),-valuedfunctionf:ERthatsatisfiesthefollowingproperties:Capacityconstraint:ForalleE,0f(e)c(e)Flowconservation:ForallvV-{s,t},(v):thesetofedgesenteringvertexv(v):thesetofedgesleavingvertexvValueofaFlowCallFthevalueofaflowf,whereMaximum-flowProblemInput:workGwithsourcesandsinktOutput:aflowofmaximumvalueCutLetSbeasubsetofVsuchthatsSandtSC(SC=V\S),(S,SC)bethesetofedgesof(u,v)EwithuSandvSC,and(SC,S)bethesetofedgesof(u,v)EwithuSCandv(S,SC)(SC,S),thatis,Howtoproveit?ProofForvV-{s,t},SumitforvSC-{t}ConsiderAddtheabovetwoProofThatis:
算法课件lecture13章节 来自淘豆网www.taodocs.com转载请标明出处.