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)

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, Professor 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.

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