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Improved approximation algorithms for two variants of the stable marriage problem with ties

Chien-Chung Huang (Institutionen för data- och informationsteknik, Datavetenskap (Chalmers)) ; T. Kavitha
Mathematical programming (0025-5610). Vol. 154 (2015), 1-2, p. 353-380.
[Artikel, refereegranskad vetenskaplig]

We consider the problem of computing a large stable matching in a bipartite graph where each vertex ranks its neighbors in an order of preference, perhaps involving ties. Let the matched partner of u in a matching M be M(u). A matching M is said to be stable if there is no edge (a, b) such that a is unmatched or prefers b to M(a) and similarly, b is unmatched or prefers a to M(b). While a stable matching in G can be easily computed in linear time by the Gale-Shapley algorithm, it is known that computing a maximum size stable matching is APX-hard. In this paper we first consider the case when the preference lists of vertices in A are strict while the preference lists of vertices in B may include ties. This case is also APX-hard and the current best approximation ratio known here is 25/17 which relies on solving an LP. We improve this ratio to 22/15 by a simple linear time algorithm. Here we first compute a half-integral stable matching in and then round it to an integral stable matching M. The ratio is bounded via a payment scheme that charges other components in to cover the costs of length-5 augmenting paths. There will be no length-3 augmenting paths here. We next consider the following special case of two-sided ties, where every tie length is 2. This case is known to be UGC-hard to approximate to within 4/3. We show a 10/7 approximation algorithm here that runs in linear time.

Nyckelord: Stable matching, Approximation algorithms

Denna post skapades 2016-01-07.
CPL Pubid: 229991


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Institutioner (Chalmers)

Institutionen för data- och informationsteknik, Datavetenskap (Chalmers)


Datavetenskap (datalogi)

Chalmers infrastruktur