Finding large stable matchings

Irving, R.W., and Manlove, D.F. (2009) Finding large stable matchings. Journal of Experimental Algorithmics, 14, 1.2. (doi:10.1145/1498698.1537595)

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Abstract

When ties and incomplete preference lists are permitted in the stable marriage and hospitals/residents problems, stable matchings can have different sizes. The problem of finding a maximum cardinality stable matching in this context is known to be NP-hard, even under very severe restrictions on the number, size, and position of ties. In this article, we present two new heuristics for finding large stable matchings in variants of these problems in which ties are on one side only. We describe an empirical study involving these heuristics and the best existing approximation algorithm for this problem. Our results indicate that all three of these algorithms perform significantly better than naive tie-breaking algorithms when applied to real-world and randomly-generated data sets and that one of the new heuristics fares slightly better than the other algorithms, in most cases. This study, and these particular problem variants, are motivated by important applications in large-scale centralized matching schemes.

Item Type:Articles
Additional Information:© ACM, 2009. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Journal of Experimental Algorithmics (14, 2009) http://doi.acm.org/10.1145/1498698.1537595
Keywords:Stable marriage, heuristics, matching schemes
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Dr David and Irving, Dr Robert
Authors: Irving, R.W., and Manlove, D.F.
Subjects:Q Science > QA Mathematics > QA75 Electronic computers. Computer science
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Journal of Experimental Algorithmics
ISSN:1084-6654
ISSN (Online):1084-6654
Published Online:01 December 2009
Copyright Holders:Copyright © 2009 Association for Computing Machinery
First Published:First published in Journal of Experimental Algorithmics 14:1.2
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
320021Algorithmics of Stable Matching Problems with IndifferenceDavid ManloveEngineering & Physical Sciences Research Council (EPSRC)GR/R84597/01Computing Science
436361MATCH-UP - matching under preferences - algorithms and complexityRobert IrvingEngineering & Physical Sciences Research Council (EPSRC)EP/E011993/1Computing Science