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 |
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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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