Abraham, D. J., Levavi, A., Manlove, D. F. 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. ISBN 9783540771043 (doi: 10.1007/978-3-540-77105-0_48)
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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, 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, Professor David and O'Malley, Dr 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 |
| Research Group: | Formal Analysis, Theory and Algorithms |
| Journal Name: | Lecture Notes in Computer Science |
| Publisher: | Springer |
| ISSN: | 0302-9743 |
| ISBN: | 9783540771043 |
| 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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