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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 dont 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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