Transcription of Network Flow Problems - Stanford University
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Network Flow Problems - Stanford University
Network Flow ProblemsJaehyun ParkCS 97 SIStanford UniversityJune 29, 2015 OutlineNetwork Flow ProblemsFord-Fulkerson AlgorithmBipartite MatchingMin-cost Max-flow AlgorithmNetwork Flow Problems2 Network Flow problem A type of Network optimization problem Arise in many different contexts (CS 261): Networks: routing as many packets as possible on a givennetwork Transportation: sending as many trucks as possible, whereroads have limits on the number of trucks per unit time Bridges: destroying (?!) some bridges to disconnectsfromt,while minimizing the cost of destroying the bridgesNetwork Flow Problems3 Network Flow problem Settings: Given a directed graphG= (V, E), where each edgeeis associated with its capacityc(e)>0.
after removing the edges, there is no path from s to t The cost of removing e is equal to its capacity c(e) The minimum cut problem is to find a cut with minimum total cost Theorem: (maximum flow) = (minimum cut) Take CS 261 if you want to …
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