L03-bipartite - Bipartite Matching Lecture 3: Jan 17 1...

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1 Bipartite Matching Lecture 3: Jan 17
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2 Bipartite Matching A graph is bipartite if its vertex set can be partitioned into two subsets A and B so that each edge has one endpoint in A and the other endpoint in B. A matching M is a subset of edges so that every vertex has degree at most one in M. A B
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3 The bipartite matching problem: Find a matching with the maximum number of edges. Maximum Matching A perfect matching is a matching in which every vertex is matched. The perfect matching problem: Is there a perfect matching?
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4 Greedy method? (add an edge with both endpoints unmatched ) First Try
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5 Key Questions How to tell if a graph does not have a (perfect) matching? How to determine the size of a maximum matching? How to find a maximum matching efficiently?
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Hall’s Theorem [1935]: A bipartite graph G=(A,B;E) has a matching that “saturates” A if and only if |N(S)| >= |S| for every subset S of A. S
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This note was uploaded on 10/13/2009 for the course CS 5150 taught by Professor Xulei during the Spring '09 term at University of Central Arkansas.

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L03-bipartite - Bipartite Matching Lecture 3: Jan 17 1...

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