The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
A necessary and sufficient condition for the existence of a complete stable matching
Journal of Algorithms
On-line algorithms for weighted bipartite matching and stable marriages
Theoretical Computer Science
An improved approximation lower bound for finding almost stable maximum matchings
Information Processing Letters
Size versus stability in the marriage problem
Theoretical Computer Science
Almost Stable Matchings by Truncating the Gale–Shapley Algorithm
Algorithmica - Special Issue: Matching Under Preferences; Guest Editors: David F. Manlove, Robert W. Irving and Kazuo Iwama
The hospitals/residents problem with quota lower bounds
ESA'11 Proceedings of the 19th European conference on Algorithms
“Almost stable” matchings in the roommates problem
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Complementary cooperation, minimal winning coalitions, and power indices
Theoretical Computer Science
Virtual Machine Coscheduling: A Game Theoretic Approach
UCC '13 Proceedings of the 2013 IEEE/ACM 6th International Conference on Utility and Cloud Computing
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An instance of the classical Stable Roommates problem need not admit a stable matching. Previous work has considered the problem of finding a matching that is ''as stable as possible'', i.e., admits the minimum number of blocking pairs. It is known that this problem is NP-hard and not approximable within n^1^2^-^@e, for any @e0, unless P=NP, where n is the number of agents in a given instance. In this paper, we extend the study to the Stable Roommates problem with Incomplete lists. In particular, we consider the case that the lengths of the lists are bounded by some integer d. We show that, even if d=3, there is some c1 such that the problem of finding a matching with the minimum number of blocking pairs is not approximable within c unless P=NP. On the other hand, we show that the problem is solvable in polynomial time for d@?2, and we give a (2d-3)-approximation algorithm for fixed d=3. If the given lists satisfy an additional condition (namely the absence of a so-called elitist odd party-a structure that is unlikely to exist in general), the performance guarantee improves to 2d-4.