Modelling and Solving the Stable Marriage Problem Using Constraint Programming

Manlove, D. F. and O'Malley, G. (2005) Modelling and Solving the Stable Marriage Problem Using Constraint Programming. In: Fifth Workshop on Modelling and Solving Problems with Constraints, Edinburgh, Scotland, 30 Jul - 05 Aug 2005, pp. 10-17.

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Abstract

We study the Stable Marriage problem (SM), which is a combinatorial problem that arises in many practical applications. We present two new models of an instance I of SM with n men and n women as an instance J of a Constraint Satisfaction Problem. We prove that establishing arc consistency in J yields the same structure as given by the established Extended Gale/Shapley algorithm for SM as applied to I. Consequently, a solution (stable matching) of I can be derived without search. Furthermore we show that, in both encodings, all stable matchings in I may be enumerated in a failure-free manner. Our first encoding is of O(n^3) complexity and is very natural, whilst our second model, of O(n^2) complexity (which is optimal), is a development of the Boolean encoding in [6], establishing a greater level of structure.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Professor David and O'Malley, Dr Gregg
Authors: Manlove, D. F., and O'Malley, G.
College/School:College of Science and Engineering > School of Computing Science
Copyright Holders:Copyright © 2005 The Authors
First Published:First published in Fifth Workshop on Modelling and Solving Problems with Constraints: 10-17
Publisher Policy:Reproduced with the permission of the Authors

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
320021Algorithmics of Stable Matching Problems with IndifferenceDavid ManloveEngineering and Physical Sciences Research Council (EPSRC)GR/R84597/01COM - COMPUTING SCIENCE