The stable roommates problem with ties

Irving, R. W. and Manlove, D.F. (2002) The stable roommates problem with ties. Journal of Algorithms, 43(1), pp. 85-105. (doi: 10.1006/jagm.2002.1219)

Abstract

We study the variant of the well-known stable roommates problem in which participants are permitted to express ties in their preference lists. In this setting, more than one definition of stability is possible. Here we consider two of these stability criteria, so-called super-stability and weak stability. We present a linear–time algorithm for finding a super-stable matching if one exists, given a stable roommates instance with ties. This contrasts with the known NP-hardness of the analogous problem under weak stability. We also extend our algorithm to cope with preference lists that are incomplete and/or partially ordered. On the other hand, for a given stable roommates instance with ties and incomplete lists, we show that the weakly stable matchings may be of different sizes and the problem of finding a maximum cardinality weakly stable matching is NP-hard, though approximable within a factor of 2.

• Item Type: Articles
• Keywords: stable matching problem; indifference; super-stability; weak stability; linear–time algorithm; NP-completeness; approximation algorithm
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Manlove, Professor David
• Authors: Irving, R. W., and Manlove, D.F.
• 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: Journal of Algorithms
• Publisher: Elsevier
• ISSN: 0196-6774
• Copyright Holders: ©2002 Elsevier Science (USA).
• First Published: First published in Journal of Algorithms 43(1):85-105
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.