非均匀稳定匹配

arXiv - CS - Computer Science and Game Theory Pub Date : 2024-08-29 DOI:arxiv-2408.16271

Naoyuki Kamiyama

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引用次数: 0

摘要

超稳定性和强稳定性是有领带的稳定匹配问题中匹配的属性。在本文中，我们引入了超稳定性和强稳定性的一般化，我们称之为非均匀稳定性。首先，我们证明可以在多项式时间内确定非均匀稳定匹配的存在性。接着，我们给出了非均匀稳定匹配集合的多面体特征。最后，我们证明非均匀稳定匹配集合构成了一个分布晶格。

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Non-uniformly Stable Matchings

Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability. First, we prove that we can determine the existence of a non-uniformly stable matching in polynomial time. Next, we give a polyhedral characterization of the set of non-uniformly stable matchings. Finally, we prove that the set of non-uniformly stable matchings forms a distributive lattice.

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arXiv - CS - Computer Science and Game Theory

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