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Perfectly matchable subgraph problem on a bipartite graph

Published online by Cambridge University Press:  08 February 2010

Firdovsi Sharifov
Firdovsi Sharifov*
Affiliation:
Glushkov Institute of Cybernetics, Glushkova pr. 40, MSP, 252650 Kyiv, Ukraine; [email protected]
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Abstract

We consider the maximum weight perfectly matchable subgraph problemon a bipartite graph G=(UV,E) with respect to given nonnegativeweights of its edges. We show that G has a perfect matching if andonly if some vector indexed by the nodes in UV is a base of anextended polymatroid associated with a submodular function definedon the subsets of UV. The dual problem of the separation problemfor the extended polymatroid is transformed to the special maximumflow problem on G. In this paper, we give a linear programmingformulation for the maximum weight perfectly matchable subgraphproblem and propose an O(n 3) algorithm to solve it.

Keywords

Bipartite graphextended polymatroidperfect matchingperfectly matchable subgraph
Type
Research Article
Information
RAIRO - Operations Research , Volume 44 , Issue 1 , January 2010 , pp. 27 - 42
Copyright
© EDP Sciences, ROADEF, SMAI, 2010

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