A Constraint Programming Approach to the Stable Marriage Problem
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- 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: Walsh T. (eds) Principles and Practice of Constraint Programming — CP 2001. CP 2001. Lecture Notes in Computer Science, vol 2239. Springer, Berlin, Heidelberg
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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