The stable roommates problem with globally-ranked pairs

Abraham, D.J., Levavi, A., Manlove, D.M. and O'Malley, G. (2007) The stable roommates problem with globally-ranked pairs. In: Proceedings of WINE 2007: 3rd International Workshop On Internet and Network Economics, San Diego, California, 12-14 December 2007, pp. 431-444. (doi:10.1007/978-3-540-77105-0_48)

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Publisher's URL: http://dx.doi.org/10.1007/978-3-540-77105-0_48

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, 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 the algorithm due to Irving et al. [R.W. Irving, D. Michail, K. Mehlhorn, K. Paluch, and K. Telikepalli. Rank-maximal matchings. ACM Transactions on Algorithms, 2(4):602-610, 2006.] to a non-bipartite setting. Also, we prove 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:Conference Proceedings
Keywords:globally-acylic preferences; symmetric preferences; rank-maximal; egalitarian; minimum regret
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Dr David and O'Malley, Dr Gregg
Authors: Abraham, D.J., Levavi, A., Manlove, D.M., 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
Research Group:Formal Analysis, Theory and Algorithms
Journal Name:Lecture Notes in Computer Science
Publisher:Springer
ISSN:0302-9743
Copyright Holders:Copyright © 2007 Springer
First Published:First published in Lecture Notes in Computer Science 4858:431-444
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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