发表机构
Institute of Science Tokyo（东京科学大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究具有最小效用差距的稳定匹配问题，通过旋转偏序集表示稳定匹配集，给出针对最大最小效用差和比率两种情况的多项式时间算法，阐明与现有框架关系并确定特殊情况。
AI 中文摘要
我们引入了具有最小效用差距的稳定匹配问题，该问题旨在寻找一种稳定匹配，使个体代理获得的效用尽可能平衡。我们的框架可以处理多对多匹配以及与代理偏好一致的伙伴集上的一般效用函数。我们考虑了两种比较代理效用的度量：最大效用与最小效用之差及其比率。我们为这两个版本都提供了多项式时间算法。该算法利用了稳定匹配集的旋转偏序集表示，特别是影响每个代理的旋转在此偏序集中形成链这一事实。为了定位我们的结果，我们还阐明了它与现有框架的关系：我们表明最近的最小割可表示性框架未涵盖我们的目标，同时确定了一个允许次模函数最小化解释的特殊情况。
英文摘要
We introduce the Stable Matching Problem with Minimum Utility Gap, which seeks a stable matching in which the utilities received by individual agents are as balanced as possible. Our framework can handle many-to-many matchings and general utility functions on partner sets that are consistent with the agents' preferences. We consider two measures for comparing agents' utilities: the difference between the maximum and minimum utilities, and their ratio. We provide a polynomial-time algorithm for both versions. The algorithm exploits the rotation-poset representation of the set of stable matchings and, in particular, the fact that the rotations affecting each agent form a chain in this poset. To position our result, we also clarify its relation to existing frameworks: we show that our objectives are not captured by the recent minimum-cut representability framework, while identifying a special case that admits a submodular function minimization interpretation.
Commentsv2: Minor revisions from v1. To appear in ISAAC 2026
