Morphing Between Stable Matching Problems

McCreesh, C., Prosser, P. and Trimble, J. (2016) Morphing Between Stable Matching Problems. In: CP 2016: 22nd International Conference on Principles and Practices of Constraint Programming, Toulouse, France, 5-9 Sept 2016, pp. 832-840. ISBN 9783319449524 (doi:10.1007/978-3-319-44953-1_52)

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Abstract

In the stable roommates (SR) problem we have n agents, where each agent ranks all other agents in strict order of preference. The problem is then to match agents into pairs such that no two agents prefer each other to their matched partners, and this is a stable matching. The stable marriage (SM) problem is a special case of SR, where we have two equal sized sets of agents, men and women, where men rank only women and women rank only men. Every instance of SM admits at least one stable matching, whereas for SR as the number of agents increases the number of instances with stable matchings decreases. So, what will happen if in SM we allow men to rank men and women to rank women, i.e. we relax gender separation? Will stability abruptly disappear? And what happens in a stable roommates scenario if agents do not rank all other agents? Again, is stability uncommon? And finally, what happens if there are an odd number of agents? We present empirical evidence to answer these questions.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Prosser, Dr Patrick and Mccreesh, Dr Ciaran
Authors: McCreesh, C., Prosser, P., and Trimble, J.
College/School:College of Science and Engineering > School of Computing Science
ISSN:0302-9743
ISBN:9783319449524
Published Online:23 August 2016
Copyright Holders:Copyright © 2016 Springer International Publishing
First Published:First published in Lecture Notes in Computer Science 9892: 832-840
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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