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Unformatted text preview: CMSC 451: Maximum Bipartite Matching Slides By: Carl Kingsford Department of Computer Science University of Maryland, College Park Based on Section 7.5 of Algorithm Design by Kleinberg & Tardos. Network Flows s u v t x w 20 10 30 20 5 30 10 20 10 10 5 15 15 5 10 The network flow problem is itself interesting. But even more interesting is how you can use it to solve many problems that don’t involve flows or even networks. Bipartite Graphs • Suppose we have a set of people L and set of jobs R . • Each person can do only some of the jobs. • Can model this as a bipartite graph → u x L R People Tasks P e rs o n u c a n d o ta s k x Bipartite Matching • A matching gives an assignment of people to tasks. • Want to get as many tasks done as possible. • So, want a maximum matching : one that contains as many edges as possible. • (This one is not maximum.) a b c d e 1 2 3 4 5 L R People Tasks Maximum Bipartite Matching Maximum Bipartite Matching Given a bipartite graph G = ( A ∪ B , E ), find an S ⊆ A × B that is a matching and is as large as possible.a matching and is as large as possible....
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 Fall '07
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 Bipartite graph, net flow, bipartite matching

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