Improved Paths to Stability for the Stable Marriage Problem
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The stable marriage problem requires one to find a marriage with no blocking pair. Given a matching that is not stable, Roth and Vande Vate have shown that there exists a sequence of matchings that leads to a stable matching in which each successive matching is obtained by satisfying a blocking pair. The sequence produced by Roth and Vande Vate's algorithm is of length O(n^3) where n is the number of men (and women). In this paper, we present an algorithm that achieves stability in a sequence of matchings of length O(n^2). We also give an efficient algorithm to find the stable matching closest to the given initial matching under an appropriate distance function between matchings.
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