The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Stable marriage and indifference
CO89 Selected papers of the conference on Combinatorial Optimization
Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
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
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While the original stable marriage problem requires all participants to rank all members of the opposite sex in a strict order, two natural variations are to allow for incomplete preference lists and ties in the preferences. Either variation is polynomially solvable, but it has recently been shown to be NP-hard to find a maximum cardinality stable matching when both of the variations are allowed. It is easy to see that the size of any two stable matchings differ by at most a factor of two, and so, an approximation algorithm with a factor two is trivial. In this paper, we give a first nontrivial result for the approximation with factor less than two. Our randomized algorithm achieves a factor of 10/7 for a restricted but still NP-hard case, where ties occur in only men's lists, each man writes at most one tie, and the length of ties is two. Furthermore, we show that these restrictions except for the last one can be removed without increasing the approximation ratio too much.