Irving, R. W. and Manlove, D.F. (2002) The stable roommates problem with ties. Journal of Algorithms, 43(1), pp. 85105. (doi:10.1006/jagm.2002.1219)

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Publisher's URL: http://dx.doi.org/doi:10.1006/jagm.2002.1219
Abstract
We study the variant of the wellknown 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, socalled superstability and weak stability. We present a linear–time algorithm for finding a superstable matching if one exists, given a stable roommates instance with ties. This contrasts with the known NPhardness 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 NPhard, though approximable within a factor of 2.
Item Type:  Articles 

Keywords:  stable matching problem; indifference; superstability; weak stability; linear–time algorithm; NPcompleteness; approximation algorithm 
Status:  Published 
Refereed:  Yes 
Glasgow Author(s) Enlighten ID:  Manlove, Dr 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:  01966774 
Copyright Holders:  ©2002 Elsevier Science (USA). 
First Published:  First published in Journal of Algorithms 43(1):85105 
Publisher Policy:  Reproduced in accordance with the copyright policy of the publisher. 
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