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Fair Matchings and Related Problems

Chien-Chung Huang (Institutionen för data- och informationsteknik, Datavetenskap (Chalmers)) ; T. Kavitha ; K. Mehlhorn ; D. Michail
Algorithmica (0178-4617). Vol. 74 (2016), 3, p. 1184-1203.
[Artikel, refereegranskad vetenskaplig]

Let G = (A boolean OR B, E) be a bipartite graph, where every vertex ranks its neighbors in an order of preference (with ties allowed) and let r be the worst rank used. A matching M is fair in G if it has maximum cardinality, subject to this, M matches the minimum number of vertices to rank r neighbors, subject to that, M matches the minimum number of vertices to rank (r - 1) neighbors, and so on. We show an efficient combinatorial algorithm based on LP duality to compute a fair matching in G. We also show a scaling based algorithm for the fair b-matching problem. Our two algorithms can be extended to solve other profile-based matching problems. In designing our combinatorial algorithm, we show how to solve a generalized version of the minimum weighted vertex cover problem in bipartite graphs, using a single-source shortest paths computation-this can be of independent interest.

Nyckelord: Matching under preferences, Profile-based matching, Bipartite graphs

Denna post skapades 2016-03-23.
CPL Pubid: 233641


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