The complexity of counting stable marriages
SIAM Journal on Computing
The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Faster scaling algorithms for network problems
SIAM Journal on Computing
Stable marriage and indifference
CO89 Selected papers of the conference on Combinatorial Optimization
Hard variants of stable marriage
Theoretical Computer Science
Inapproximability Results on Stable Marriage Problems
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Approximability results for stable marriage problems with ties
Theoretical Computer Science
Randomized approximation of the stable marriage problem
Theoretical Computer Science - Special papers from: COCOON 2003
A 1.875: approximation algorithm for the stable marriage problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A (2 - c1/√N)-approximation algorithm for the stable marriage problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Finding large stable matchings
Journal of Experimental Algorithmics (JEA)
A 25/17-approximation algorithm for the stable marriage problem with one-sided ties
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Two hardness results for core stability in hedonic coalition formation games
Discrete Applied Mathematics
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We consider variants of the classical stable marriage problem in which preference lists may contain ties, and may be of bounded length. Such restrictions arise naturally in practical applications, such as centralised matching schemes that assign graduating medical students to their first hospital posts. In such a setting, weak stability is the most common solution concept, and it is known that weakly stable matchings can have different sizes. This motivates the problem of finding a maximum cardinality weakly stable matching, which is known to be NP-hard in general. We show that this problem is solvable in polynomial time if each man's list is of length at most 2 (even for women's lists that are of unbounded length). However if each man's list is of length at most 3, we show that the problem becomes NP-hard (even if each women's list is of length at most 3) and not approximable within some @d1 (even if each woman's list is of length at most 4).