A constraint programming approach to the stable marriage problem

Gent, I. P., Irving, R.W., Manlove, D.F., Prosser, P. and Smith, B.M. (2001) A constraint programming approach to the stable marriage problem. In: Proceedings of CP '01: the 7th International Conference on Principles and Practice of Constraint Programming, Paphos, Cyprus, 26 November - 1 December, 2001, pp. 225-239. ISBN 3-540-42863-1

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.

• Item Type: Conference Proceedings
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Manlove, Professor David
• Authors: Gent, I. P., Irving, R.W., Manlove, D.F., Prosser, P., and Smith, B.M.
• Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• College/School: College of Science and Engineering > School of Computing Science
• Research Group: Formal Analysis, Theory and Algorithms
• Publisher: Springer Verlag
• ISSN: 0302-9743
• ISBN: 3-540-42863-1
• Copyright Holders: © Springer-Verlag
• First Published: First published in Lecture Notes in Computer Science 2239:225-239
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.