The stable marriage problem with master preference lists

Irving, R.W.,, Manlove, D.F., and Scott, S. (2008) The stable marriage problem with master preference lists. Discrete Applied Mathematics, 156(15), pp. 2959-2977. (doi:10.1016/j.dam.2008.01.002)

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Abstract

We study variants of the classical stable marriage problem in which the preferences of the men or the women, or both, are derived from a master preference list. This models real-world matching problems in which participants are ranked according to some objective criteria. The master list(s) may be strictly ordered, or may include ties, and the lists of individuals may involve ties and may include all, or just some, of the members of the opposite sex. In fact, ties are almost inevitable in the master list if the ranking is done on the basis of a scoring scheme with a relatively small range of distinct values. We show that many of the interesting variants of stable marriage that are NP-hard remain so under very severe restrictions involving the presence of master lists, but a number of special cases can be solved in polynomial time. Under this master list model, versions of the stable marriage problem that are already solvable in polynomial time typically yield to faster and/or simpler algorithms, giving rise to simple new structural characterisations of the solutions in these cases.

Item Type:Articles
Keywords:Stable matching, ties, weakly stable, strongly stable, super-stable
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Dr David and Irving, Dr Robert
Authors: Irving, R.W.,, Manlove, D.F., and Scott, S.
Subjects:Q Science > QA Mathematics > QA75 Electronic computers. Computer science
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Discrete Applied Mathematics
Publisher:Elsevier
ISSN:0166-218X
ISSN (Online):1872-6771
Published Online:15 February 2008
Copyright Holders:Copyright © 2008 Elsevier
First Published:First published in Discrete Applied Mathematics 156(15):2959-2977
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