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Efficient algorithms for weighted rank-maximal matchings and related problems

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

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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
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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