Sciweavers

WAOA
2005
Springer

"Almost Stable" Matchings in the Roommates Problem

14 years 5 months ago
"Almost Stable" Matchings in the Roommates Problem
An instance of the classical Stable Roommates problem (sr) need not admit a stable matching. This motivates the problem of finding a matching that is “as stable as possible”, i.e. admits the fewest number of blocking pairs. In this paper we prove that, given an sr instance with n agents, in which all preference lists are complete, the problem of finding a matching with the fewest number of blocking pairs is NP-hard and not approximable within n 1 2 −ε , for any ε > 0, unless P=NP. If the preference lists contain ties, we improve this result to n1−ε . Also, we show that, given an integer K and an sr instance I in which all preference lists are complete, the problem of deciding whether I admits a matching with exactly K blocking pairs is NP-complete. By contrast, if K is constant, we give a polynomial-time algorithm that finds a matching with at most (or exactly) K blocking pairs, or reports that no such matching exists. Finally, we give upper and lower bounds for the mi...
David J. Abraham, Péter Biró, David
Added 28 Jun 2010
Updated 28 Jun 2010
Type Conference
Year 2005
Where WAOA
Authors David J. Abraham, Péter Biró, David Manlove
Comments (0)