The stable roommates problem with globally-ranked pairs

  • Authors:

  • David J. Abraham;Ariel Levavi;David F. Manlove;Gregg O'Malley

  • Affiliations:

  • Computer Science Department, Carnegie Mellon University;Computer Science Department, Carnegie Mellon University;Department of Computing Science, University of Glasgow, UK;Department of Computing Science, University of Glasgow, UK

  • Venue:
  • WINE'07 Proceedings of the 3rd international conference on Internet and network economics
  • Year:
  • 2007

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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. [18] 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.