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. Participants list members of opposite sex they like to date.

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• Spring '09
• Bipartite graph, Maximum flow problem, Diana Diane Amy Amy Amy, Alice Bob Carol Dave Eliza Frank, Maximum bipartite matching

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