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

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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, Dr 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.

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