26_5 - Network with multiple sources and sinks 15 Maximum...

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1 Network with multiple sources and sinks Can be reduced to a single source & single sink max problem 15 14 19 30 s1 t1 a b c d 11 1 9 13 s2 t2 e b f d 5 4 12 23 s3 t3 g b h d k 9 4 s t Maximum bipartite matching ± Bipartite graph G=(V,E): ± Undirected ± V = V 1 V 2 , V 1 V 2 = . ± e=(u, v) E, u V 1 and v V 2 ± Complete bipartite: u V1, u is joined with every v V2 ± Matching: set of edges with no vertex included twice ± Maximum matching : a matching of maximum cardinality ± i.e. no matching contains more edges Applications ± Dating assignment ± L – women , R – men. ± An edge between vertices: they have a chance to be “compatible” (can be matched) ± Job placement ± Companies make job offers ± Students have job choices ± An edge between vertices: the student can fit the job Example ± Problem: Given N men and M women, find a matching between men and women.
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This document was uploaded on 02/21/2011.

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26_5 - Network with multiple sources and sinks 15 Maximum...

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