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• W2079168081 abstract "Let G = G(A∪B,A×B), with |A| = |B| = n, be a weighted bipartite graph, and let d(·,·) be the cost function on the edges. Let w(M) denote the weight of a matching in G, and M* a minimum-cost perfect matching in G. We call a perfect matching M c-approximate, for c ≥ 1, if w(M) ≤ c · w(M*). We present three approximation algorithms for computing minimum-cost perfect matchings in G. First, we consider the case when d(·,·) is a metric. For any δ > 0, we present an algorithm that, in O(n2+δ log n log2(1/δ)) time, computes a O(1/δα)-approximate matching of G, where α = log3 2 ≈ 0.631. Next, we assume the existence of a dynamic data structure for answering approximate nearest neighbor (ANN) queries under d(··). Given two parameters e, d e) is the query and update time of an (e/2)-ANN data structure. Finally, we present an algorithm that works even if d(·,·) is not a metric but admits an ANN data structure for d(·,·). In particular, we present an algorithm that computes, in O(e---1n3/2τ (n, e) log4(n/e) log Δ) time, a (1 + e)-approximate matching of A and B; here Δ is the ratio of the largest to the smallest-cost edge in G, and τ (n, e) is the query and update time of an (e/c)-ANN data structure for some constant c > 1. We show that our results lead to faster matching algorithms for many geometric settings." @default.
• W2079168081 created "2016-06-24" @default.
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• W2079168081 date "2014-05-31" @default.
• W2079168081 modified "2023-09-29" @default.
• W2079168081 title "Approximation algorithms for bipartite matching with metric and geometric costs" @default.
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• W2079168081 doi "https://doi.org/10.1145/2591796.2591844" @default.
• W2079168081 hasPublicationYear "2014" @default.
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