The stable roommates problem with globally-ranked pairs

Abraham, D.J., Levavi, A., Manlove, D.F. and O'Malley, G. (2008) The stable roommates problem with globally-ranked pairs. Internet Mathematics, 5(4), pp. 493-515.

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Abstract

We introduce a restriction of the stable roommates problem in which roommate pairs are ranked globally. In contrast to the unrestricted problem, weakly stable matchings are guaranteed to exist, and additionally, they can be found in polynomial time. However, it is still the case that strongly stable matchings may not exist, and so we consider the complexity of finding weakly stable matchings with various desirable properties. In particular, we present a polynomial-time algorithm to find a rank-maximal (weakly stable) matching. This is the first generalization of an algorithm due to [Irving et al. 06] to a nonbipartite setting. Also, we describe several hardness results in an even more restricted setting for each of the problems of finding weakly stable matchings that are of maximum size, are egalitarian, have minimum regret, and admit the minimum number of weakly blocking pairs.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Dr David and O'Malley, Mr Gregg
Authors: Abraham, D.J., Levavi, A., 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:Internet Mathematics
Publisher:A.K. Peters
ISSN:1542-7951
ISSN (Online):1944-9488
Published Online:26 February 2010
Copyright Holders:Copyright © 2008 A.K. Peters
First Published:First published in Internet Mathematics 5(4):493-515
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