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)

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, Professor 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.

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
32002	1	Algorithmics of Stable Matching Problems with Indifference	David Manlove	Engineering & Physical Sciences Research Council (EPSRC)	GR/R84597/01	Computing Science
43636	1	MATCH-UP - matching under preferences - algorithms and complexity	Robert Irving	Engineering & Physical Sciences Research Council (EPSRC)	EP/E011993/1	Computing Science