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Lecture 20 Max-Flow Problem and Augmenting Path Algorithm

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Lecture 20Max-Flow Problemand Augmenting path AlgorithmOctober 28, 2009Lecture 20Outline Max-Flow Problem Description Some examples Algorithm for solving Max-Flow Problem Augmenting path algorithmOperations Research Methods1Lecture 20Max-Flow Problem : Single-Source Single-SinkWe are given a directed capacitated network(V, E, C)connecting a source(origin) node with a sink (destination) setVis the set of nodes in the setEis the set of directed links(i, j)The setCis the set of capacitiescij 0of the links(i, j) Problem is to determine themaximum amount of flowthat can besent from the source node to the sink isMax-Flow Problemfor single-source and single-sinkOperations Research Methods2Lecture 20Max-Flow Problem : Multiple-Sources Multiple-SinksWe are given a directed capacitated network(V, E, C)connecting multiplesource nodes with multiple sink setVis the set of nodes and the setEis the set of directed links(i, j)The setCis the set of capacitiescij 0of the links(i, j) EThe Problem is to determine themaximum amount of flowthat can besent from the source nodes to the sink isMax-Flow Problemfor multiple-sources and multiple-sinksOperations Research Methods3Lecture 20Multiple-sources multiple-links Problem can be converted to a single-sourceand single-sink Problem by Introduci

of the path In other words, the capacity of a path is the maximum possible amount that we can send along the path The capacity C(p) of the path p is given by C(p) = min (i,j)∈p u ij where u ij is the capacity of the link (i,j) If the path p under consideration …

  Path, A path

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