Approximation algorithms for hard variants of the stable marriage and hospitals/residents problems

Irving, R.W. and Manlove, D.F. (2008) Approximation algorithms for hard variants of the stable marriage and hospitals/residents problems. Journal of Combinatorial Optimization, 16(3), pp. 279-292. (doi: 10.1007/s10878-007-9133-x)

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 paper, we describe polynomial-time 5/3-approximation algorithms for variants of these problems in which ties are on one side only and at the end of the preference lists. The particular variant is motivated by important applications in large scale centralised matching schemes.

• Item Type: Articles
• Additional Information: The original publication is available at www.springerlink.com
• Keywords: Stable matching, weak stability, NP-hard problems, approximation algorithms
• 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 Combinatorial Optimization
• Publisher: Springer
• ISSN: 1382-6905
• ISSN (Online): 1573-2886
• Published Online: 23 December 2007
• Copyright Holders: Copyright © 2008 Springer Verlag
• First Published: First published in Journal of Combinatorial Optimization 16(3):279-292
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher including additional information statement.

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