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)

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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<sup>1−ε</sup>, 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 A later version of this paper is available via the Related URL link.
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
ISSN (Online):1611-3349
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 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