Stable marriage with ties and bounded length preference lists

Irving, R.W., Manlove, D.F. and O'Malley, G. (2009) Stable marriage with ties and bounded length preference lists. Journal of Discrete Algorithms, 7(2), pp. 213-219. (doi:10.1016/j.jda.2008.09.003)

Irving, R.W., Manlove, D.F. and O'Malley, G. (2009) Stable marriage with ties and bounded length preference lists. Journal of Discrete Algorithms, 7(2), pp. 213-219. (doi:10.1016/j.jda.2008.09.003)

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Publisher's URL: http://dx.doi.org/10.1016/j.jda.2008.09.003

Abstract

We consider variants of the classical stable marriage problem in which preference lists may contain ties, and may be of bounded length. Such restrictions arise naturally in practical applications, such as centralised matching schemes that assign graduating medical students to their first hospital posts. In such a setting, weak stability is the most common solution concept, and it is known that weakly stable matchings can have different sizes. This motivates the problem of finding a maximum cardinality weakly stable matching, which is known to be NP-hard in general. We show that this problem is solvable in polynomial time if each man's list is of length at most 2 (even for women's lists that are of unbounded length). However if each man's list is of length at most 3, we show that the problem becomes NP-hard (even if each women's list is of length at most 3) and not approximable within some δ>1 (even if each woman's list is of length at most 4).

Item Type:Articles
Keywords:Stable marriage problem, ties, incomplete lists, NP-hardness, polynomial-time algorithm
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Professor David and O'Malley, Mr Gregg and Irving, Dr Robert
Authors: Irving, R.W., Manlove, D.F., and O'Malley, G.
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 Discrete Algorithms
Publisher:Elsevier
ISSN:1570-8667
ISSN (Online):1570-8675
Published Online:20 September 2008
Copyright Holders:Copyright © 2009 Elsevier
First Published:First published in Journal of Discrete Algorithms 7(2):213-219
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/E011993/1COM - COMPUTING SCIENCE