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)
The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
The Geometry of Fractional Stable Matchings and its Applications
Mathematics of Operations Research
A fixed-point approach to stable matchings and some applications
Mathematics of Operations Research
Finding a Level Ideal of a Poset
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
SIAM Journal on Discrete Mathematics
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Let I be a stable matching instance with N stable matchings. For each man m, order his N stable partners from his most preferred to his least preferred. Denote the ith woman in his sorted list as pi(m). Let αi consist of the man-woman pairs where each man m is matched to pi(m). Teo and Sethuraman proved this surprising result: for i = 1 to N, not only is αi a matching, it is also stable. The αi's are called the generalized median stable matchings of I. In this paper, we present a new characterization of these stable matchings that is solely based on I's rotation poset. We then prove the following: when i = O(log n), where n is the number of men, αi can be found efficiently; but when i is a constant fraction of N, finding αi is NP-hard. We also consider what it means to approximate the median stable matching of I, and present results for this problem.