Stable Marriage with Ties and Bounded Length Preference Lists

Irving, R. W., Manlove, D. F. and O'Malley, G. (2006) Stable Marriage with Ties and Bounded Length Preference Lists. In: Algorithms and Complexity in Durham 2006: Proceedings of the Second ACiD Workshop, Durham, UK, 18-20 Sep 2006, pp. 95-106. ISBN 9781904987383

Irving, R. W., Manlove, D. F. and O'Malley, G. (2006) Stable Marriage with Ties and Bounded Length Preference Lists. In: Algorithms and Complexity in Durham 2006: Proceedings of the Second ACiD Workshop, Durham, UK, 18-20 Sep 2006, pp. 95-106. ISBN 9781904987383

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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 and not approximable within some d > 1, even if each woman's list is of length at most 4.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Irving, Dr Robert and Manlove, Professor David and O'Malley, Dr Gregg
Authors: Irving, R. W., Manlove, D. F., and O'Malley, G.
College/School:College of Science and Engineering > School of Computing Science
ISBN:9781904987383
Copyright Holders:Copyright © 2006 The Authors
First Published:First published in Algorithms and Complexity in Durham 2006: Proceedings of the Second ACiD Workshop: 95-106
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
320021Algorithmics of Stable Matching Problems with IndifferenceDavid ManloveEngineering and Physical Sciences Research Council (EPSRC)GR/R84597/01COM - COMPUTING SCIENCE