Computing at Glasgow University
Paper ID: 8709
DCS Tech Report Number: TR-2007-257

The Stable Roommates problem with Globally-Ranked Pairs
Abraham,D.J. Levavi,A. Manlove,D.F. O'Malley,G.

Publication Type: Tech Report (internal)
Appeared in: DCS Technical Report Series
Page Numbers :
Publisher: Dept of Computing Science, University of Glasgow
Year: 2007

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.

Keywords: globally-acylic preferences; symmetric preferences; rank-maximal; egalitarian; minimum regret

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