发表机构
Inria and DI ENS, École Normale Supérieure PSL University（法国国家数字与能源研究所及信息与智能系统研究院，巴黎文理研究大学高等师范学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究超图随机匹配中稳定性的充要条件，引入在线分配策略，证明其是对贪婪策略的良好推广，能推导稳定性充要条件并给出与到达率无关的最大稳定策略。
AI 中文摘要
超图上的随机匹配因其在捕捉现实生活系统（从活体捐赠移植到拼车）中的通用性而成为一个重要课题。然而，找到稳定性的充要条件是一个长期存在的问题。关键困难之一是，贪婪策略虽然在图的随机匹配中具有最大稳定性，但在超图上不再能达到最大稳定区域。到目前为止，还没有已知的具有类似性质的替代策略族。在这项工作中，我们引入了在线分配策略，即每个项目在到达时被分配到一个匹配的超边类型。我们通过证明它们具有最大稳定性，表明这是对贪婪策略的良好推广。它们易于分析的特性使我们能够推导出几个稳定性的充要条件，这些条件推广了已知的图的条件。此外，构造性证明给出了一个与到达率无关的最大稳定策略。
英文摘要
Stochastic matching on hypergraphs is an important topic for its versatility in capturing real-life systems, from living donor transplant to ride-hailing. Nevertheless, finding necessary and sufficient criteria for stability is a long-standing problem. One of the key difficulties is the fact that greedy policies, whilst maximally stable for stochastic matching on graphs, no longer achieve maximal stability region on hypergraphs. So far, no alternative families of policies with similar properties have been known. In this work, we introduce online assignment policies, in which each item is assigned to a matching hyperedge type upon arrival. We show that this is a good generalisation to greedy policies, by proving that they are maximally stable. Their natural amenability to analysis allow us to derive several necessary and sufficient criteria for stability, which generalise the known criteria for graphs. Furthermore, the constructive proof gives a maximally stable arrival-rate agnostic policy.
