Modifying an instance of the super-stable matching problem

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters Pub Date : 2024-11-27 DOI:10.1016/j.ipl.2024.106549

Naoyuki Kamiyama

引用次数: 0

Abstract

The topic of this paper is the stable matching problem in a bipartite graph. Super-stability is one of the stability concepts in the stable matching problem with ties. It is known that there may not exist a super-stable matching, and the existence of a super-stable matching can be checked in polynomial time. In this paper, we consider the problem of modifying an instance of the stable matching problem with ties by deleting some bounded number of agents in such a way that there exists a super-stable matching in the modified instance. First, we consider the setting where we are allowed to delete agents on only one side. We prove that, in this setting, our problem can be solved in polynomial time. Interestingly, this result is obtained by carefully observing the existing algorithm for checking the existence of a super-stable matching. Next, we consider the setting where we are given an upper bound on the number of deleted agents for each side, and we are allowed to delete agents on both sides. We prove that, in this setting, our problem is NP-complete.

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修改一个超稳定匹配问题的实例

本文的主题是二部图的稳定匹配问题。超稳定是带联系的稳定匹配问题中的一个稳定概念。已知可以不存在超稳定匹配，并且可以在多项式时间内检验是否存在超稳定匹配。本文考虑通过删除有限数量的智能体，使修改后的实例中存在一个超稳定的匹配，从而修改一个有约束的稳定匹配问题的实例。首先，我们考虑只允许在一侧删除代理的设置。我们证明，在这种情况下，我们的问题可以在多项式时间内解决。有趣的是，这个结果是通过仔细观察现有的超稳定匹配是否存在的算法得到的。接下来，我们考虑这样一种设置，在这种设置中，我们被给定了每一边被删除代理数量的上限，并且我们被允许删除两边的代理。我们证明，在这种情况下，我们的问题是np完全的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Information Processing Letters 工程技术-计算机：信息系统

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

7.3 months

期刊介绍： Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered. Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.