Size versus stability in the marriage problem

Biro, P., Manlove, D.F. and Mittal, S. (2009) Size versus stability in the marriage problem. In: Approximation and Online Algorithms. Springer, pp. 15-28. ISBN 9783540939795 (doi: 10.1007/978-3-540-93980-1_2)

Abstract

Given an instance <i>I</i> of the classical Stable Marriage problem with Incomplete preference lists (smi), a maximum cardinality matching can be larger than a stable matching. In many large-scale applications of smi, we seek to match as many agents as possible. This motivates the problem of finding a maximum cardinality matching in <i>I</i> that admits the smallest number of blocking pairs (so is "as stable as possible"). We show that this problem is NP-hard and not approximable within n^1−ε, for any ε > 0, unless P=NP, where <i>n</i> is the number of men in <i>I</i>. Further, even if all preference lists are of length at most 3, we show that the problem remains NP-hard and not approximable within δ, for some δ > 1. By contrast, we give a polynomial-time algorithm for the case where the preference lists of one sex are of length at most 2.

• Item Type: Book Sections
• Additional Information: The original publication is available at www.springerlink.com. A later version of this paper is available via the Related URL link.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Manlove, Professor David and Biro, Dr Peter
• Authors: Biro, P., Manlove, D.F., and Mittal, S.
• Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Lecture Notes in Computer Science
• Publisher: Springer
• ISSN: 0302-9743
• ISSN (Online): 1611-3349
• ISBN: 9783540939795
• Published Online: 13 January 2009
• Copyright Holders: Copyright © 2009 Springer
• First Published: First published in Lecture Notes in Computer Science 5426:15-28
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher

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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