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- W1736880087 abstract "We consider the problem of designing efficient algorithms for computing certain matchings in a bipartite graph $G =({mathcal{A}} cup {mathcal{P}}, {mathcal{E}})$ , with a partition of the edge set as ${mathcal{E}} = {mathcal{E}}_1 {mathbin {dot{cup}}} {mathcal{E}}_2 ldots {mathbin {dot{cup}}} {mathcal{E}}_r$ . A matching is a set of (a, p) pairs, $a in {mathcal{A}}, pin{mathcal{P}}$ such that each a and each p appears in at most one pair. We first consider the popular matching problem; an $O(msqrt{n})$ 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(n ω ) randomized algorithm for this problem, where ω< 2.376 is the exponent of matrix multiplication. We next consider the rank-maximal matching problem; an $O(min(mn,Cmsqrt{n}))$ algorithm was given in [7] for this problem. Here we give an O(Cn ω ) 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 ${mathcal{A}}$ have positive weights." @default.
- W1736880087 created "2016-06-24" @default.
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- W1736880087 date "2006-01-01" @default.
- W1736880087 modified "2023-09-27" @default.
- W1736880087 title "Efficient Algorithms for Weighted Rank-Maximal Matchings and Related Problems" @default.
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- W1736880087 doi "https://doi.org/10.1007/11940128_17" @default.
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