A contraint programming approach to the stable marriage problem

Gent, Ian P., Irving, Robert W., Manlove, David F., Prosser, Patrick and Smith, Barbara M. (2001) A contraint programming approach to the stable marriage problem. In: Principles and Practice of Constraint Programming - CP 2001. Lecture Notes in Computer Science, 2239 . Springer-Verlag, pp. 225-239. ISBN 9783540428633

Abstract

The Stable Marriage problem (SM) is an extensively-studied combinatorial problem with many practical applications. In this paper we present two encodings of an instance I of SM as an instance J of a Constraint Satisfaction Problem. We prove that, in a precise sense, establishing arc consistency in J is equivalent to the action of the established Extended Gale/Shapley algorithm for SM on I. As a consequence of this, the man-optimal and woman-optimal stable matchings can be derived immediately. Furthermore we show that, in both encodings, all solutions of I may be enumerated in a failure-free manner. Our results indicate the applicability of Constraint Programming to the domain of stable matching problems in general, many of which are NP-hard.

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