UNIVERSITY of GLASGOW

Computing at Glasgow University
 
Paper ID: 9319

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

Publication Type: Journal
Appeared in: Internet Mathematics, volume 5, number 4
Page Numbers : 493-515
Publisher: N/A
Year: 2008
ISBN/ISSN:

URL: This publication is available at this URL.

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 describe 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: Stable Roommates problem; Globally ranked pairs; Rank-maximal matchings; Egalitarian weakly stable matching


PDF Bibtex entry Endnote XML