A Constraint Programming Approach to the Stable Marriage Problem
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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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- A Constraint Programming Approach to the Stable Marriage Problem
- Book Title
- Principles and Practice of Constraint Programming — CP 2001
- Book Subtitle
- 7th International Conference, CP 2001 Paphos, Cyprus, November 26 – December 1, 2001 Proceedings
- pp 225-239
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
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- Toby Walsh (4)
- Editor Affiliations
- 4. Department of Computer Science, The University of York
- Author Affiliations
- 5. School of Computer Science, University of St. Andrews, Scotland
- 6. Department of Computing Science, University of Glasgow, Scotland
- 7. School of Computing and Mathematics, University of Huddersfield, England
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