Understanding the Generalized Median Stable Matchings

13 years 4 months ago

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Let I be a stable matching instance with N stable matchings. For each man m, order his (not necessarily distinct) N partners from his most preferred to his least preferred. Denote the ith woman in his sorted list as pi(m). Let i 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 i a matching, it is also stable. The i's are called the generalized median stable matchings of I. Determining if these stable matchings can be computed efficiently is an open problem. In this paper, we present a new characterization of the generalized median stable matchings that provides interesting insights. It implies that the generalized median stable matchings in the middle

Christine T. Cheng

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