Kavitha, Telikepalli and Shah, Chintan D
(2006)
*Efficient algorithms for weighted rank-maximal matchings and related problems.*
[Book Chapter]

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## Abstract

We consider the problem of designing efficient algorithms for computing certain matchings in a bipartite graph , with a partition of the edge set as . A matching is a set of (a, p) pairs, such that each a and each p appears in at most one pair. We first consider the popular matching problem; an algorithm to solve the popular matching problem was given in [3], where n is the number of vertices and m is the number of edges in the graph. Here we present an O(nω) randomized algorithm for this problem, where ω< 2.376 is the exponent of matrix multiplication. We next consider the rank-maximal matching problem; an algorithm was given in [7] for this problem. Here we give an O(Cnω) randomized algorithm, where C is the largest rank of an edge used in such a matching. We also consider a generalization of this problem, called the weighted rank-maximal matching problem, where vertices in have positive weights.

Item Type: | Book Chapter |
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Publication: | Algorithms and Computation |

Publisher: | Springer Verlag |

Additional Information: | The copyright belongs to Springer Verlag. |

Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |

Date Deposited: | 13 Nov 2007 |

Last Modified: | 19 Sep 2010 04:41 |

URI: | http://eprints.iisc.ac.in/id/eprint/12414 |

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