Transcription of Network Flow Problems - Stanford University
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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.
Network Flow Problem ... “subtract” our flow f. It is a valid flow of positive total flow. By the flow decomposition, it can be decomposed into flow paths and circulations. These flow paths must have been found by Ford-Fulkerson. Contradiction. Ford-Fulkerson Algorithm 10.
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