The complexity of counting stable marriages
SIAM Journal on Computing
Three fast algorithms for four problems in stable marriage
SIAM Journal on Computing
An efficient algorithm for the “optimal” stable marriage
Journal of the ACM (JACM)
Every finite distributive lattice is a set of stable matchings for a small stable marriage instance
Journal of Combinatorial Theory Series A
The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
A new fixed point approach for stable networks and stable marriages
Journal of Computer and System Sciences
Approximability results for stable marriage problems with ties
Theoretical Computer Science
Maximizing Quadratic Programs: Extending Grothendieck's Inequality
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Partially ordered knapsack and applications to scheduling
Discrete Applied Mathematics
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The stable marriage problem is a classical matching problem introduced by Gale and Shapley. It is known that for any instance, there exists a solution, and there is a polynomial time algorithm to find one. However, the matching obtained by this algorithm is man-optimal, that is, the matching is favorable for men but unfavorable for women, (or, if we exchange the roles of men and women, the resulting matching is woman-optimal). The sex-equal stable marriage problem, posed by Gusfield and Irving, seeks a stable matching “fair” for both genders. Specifically it seeks a stable matching with the property that the sum of the men's scores is as close as possible to that of the women's. This problem is known to be strongly NP-hard. In this paper, we give a polynomial time algorithm for finding a near optimal solution for the sex-equal stable marriage problem. Furthermore, we consider the problem of optimizing an additional criterion: among stable matchings that are near optimal in terms of the sex-equality, find a minimum egalitarian stable matching. We show that this problem is strongly NP-hard, and give a polynomial time algorithm whose approximation ratio is less than two.