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.

翻译：稳定匹配问题要求找到一个无阻塞对的匹配。针对非稳定匹配，Roth与Vande Vate已证明存在一系列匹配可引导至稳定匹配，其中每个相继匹配均通过满足某个阻塞对获得。Roth-Vande Vate算法生成的序列长度为$O(n^3)$，其中$n$表示男性（及女性）人数。本文提出一种算法，可在长度为$O(n^2)$的匹配序列中实现稳定性。我们同时给出一种高效算法，在恰当的匹配间距离函数下，寻找与给定初始匹配最接近的稳定匹配。