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.
CITATION STYLE
Gent, I. P., Irving, R. W., Manlove, D. F., Prosser, P., & Smith, B. M. (2001). A constraint programming approach to the stable marriage problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2239, pp. 225–239). Springer Verlag. https://doi.org/10.1007/3-540-45578-7_16
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