室友多样性问题的普及

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science Pub Date : 2024-10-15 DOI:10.1016/j.tcs.2024.114903

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引用次数: 0

摘要

室友多样性问题是多维稳定室友问题的一个新近引入的受限变体：每个代理都属于两种类型（如红色和蓝色）中的一种，代理对房间的偏好完全取决于室友中自己类型代理的比例。我们用 "受欢迎程度 "的概念研究了这一变量。我们发现，在室友多样性问题中，当房间大小固定为 2 时，问题变得很容易解决。我们的研究表明，在房间大小固定为 2 的室友多样性问题中，问题变得很容易解决。特别是，可以保证存在一个受欢迎的代理分区，并且可以在多项式时间内计算出来。此外，在任何室友多样性博弈中，都能保证存在一个混合的受欢迎的代理分区。相比之下，当室友多样性博弈的房间大小不受限制时，受欢迎的分区可能不存在，问题变得难以解决。

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Popularity on the roommate diversity problem

A recently introduced restricted variant of the multidimensional stable roommates problem is the roommate diversity problem: each agent belongs to one of two types (e.g., red and blue), and the agents' preferences over the rooms solely depend on the fraction of agents of their own type among their roommates. We study this variant with the notion of popularity.

We show that in the roommate diversity problem with the room size fixed to 2, the problem becomes tractable. Particularly, a popular partitioning of agents is guaranteed to exist and can be computed in polynomial time. Additionally, a mixed popular partitioning of agents is always guaranteed to exist in any roommate diversity game. By contrast, when there are no restrictions on the room size of a roommate diversity game, a popular partitioning may fail to exist and the problem becomes intractable.

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来源期刊

Theoretical Computer Science 工程技术-计算机：理论方法

CiteScore

2.60

自引率

18.20%

发文量

471

审稿时长

12.6 months

期刊介绍： Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.