发表机构
Inria and DI ENS, École Normale Supérieure PSL University（法国国家信息与自动化研究所与巴黎高等师范学院PSL大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对含批量到达的随机超图加权匹配问题，扩展前人成果推导了必要充分判据，提出了最大化稳定的到达率无关策略，丰富了随机超图匹配的稳定性理论。
AI 中文摘要
许多现实系统都可作为随机超图匹配的实例，比如生产线或按订单装配系统。两个常见特征是：匹配所需物品数量可能不同，且可能存在中间物品，这类物品由其他物品组合而成，而非外部到达。这两种现象都可通过考虑随机匹配的加权变体来建模。本研究将随机超图上的加权匹配概念形式化，同时允许批量到达，即同一类物品可同时到达多个。随后，我们扩展了Nguyen与Bušić（2006）的成果，以克服新设定带来的复杂问题。尽管存在诸多差异，我们仍推导了必要且充分的判据，作为非加权设定判据的直接推广。构造性证明还给出了一种最大化稳定、基于规模、与到达率无关的策略。
英文摘要
Many real-life systems can be found as examples of stochastic matching on hypergraphs, such as production lines or assemble-to-order systems. Two common features are the number of items required may vary between matchings, and there may intermediary items which exist as a combination of other items and not of external arrivals. Both of these phenomena can be modelled by considering the weighted variant of stochastic matching. In this work, we formalise the notion of stochastic weighted matching on hypergraphs. We also allow batch arrivals, meaning multiple items of multiple classes may arrive at the same time, and in particular, the arrivals can be correlated between classes. Unlike the classical setting where items arrive at discrete time $t \in \mathbb{N}$, we allow arrival processes to take place in continuous time $t \in \mathbb{R}_{\geq 0}$. We then extend the results from Nguyen and Bušić (2026) to overcome the intricacies brought up by this new setting. This allows us to derive necessary and sufficient criteria as direct generalisations of those in the unweighted setting, which depend only on the per-class arrival rates. As such, the correlation between classes bear no differences. The constructive proofs also give a maximally stable, periodic-review, size-based, arrival-rate agnostic policy.
