稳定婚姻问题的改进稳定路径
Improved Paths to Stability for the Stable Marriage Problem
AI总结：
针对稳定婚姻问题，本文提出一种将匹配序列长度从$O(n^3)$降至$O(n^2)$的稳定化算法，并给出在特定距离函数下寻找最接近初始匹配的高效算法。
摘要：
稳定婚姻问题要求找到一个没有阻挡对的婚姻。给定一个不稳定的匹配，Roth和Vande Vate已经证明存在一个匹配序列可以导向稳定匹配，其中每个后继匹配都是通过满足一个阻挡对获得的。Roth和Vande Vate算法产生的序列长度为$O(n^3)$，其中$n$是男性（和女性）的数量。在本文中，我们提出了一种算法，能够在长度为$O(n^2)$的匹配序列中实现稳定性。我们还给出了一种高效算法，在适当的匹配间距离函数下，找到最接近给定初始匹配的稳定匹配。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
