AI 中文总结
研究超图上随机动态匹配的可稳定性，通过到达率和关联矩阵刻画，将简单图相关刻画扩展到任意超边，无需一般位置假设，提出VQML策略可稳定每个可稳定实例，实现最大稳定。
AI 中文摘要
我们研究超图上的随机动态匹配：有限多个类别的物品随时间到达，并通过激活超边在多集中被移除。我们仅根据到达率和关联矩阵来刻画可稳定性，即存在一种匹配策略使队列过程为正常返的情况：(G, $\lambda$) 是可稳定的，当且仅当守恒方程 A$\mu$ = $\lambda$ 有一个非负解，其支撑诱导出一个满射子矩阵，等价地，$\lambda$ 位于由超边生成的锥的内部。这将简单图已知的刻画（非二分性以及独立集不等式）扩展到任意超边，允许有重数和单条边，并且与常数遗憾理论不同，不需要一般位置假设。充分性是构造性的：单个与 $\lambda$ 无关的策略，虚拟队列最长匹配（VQML），它是Nazari和Stolyar的扩展贪婪原始对偶策略的无奖励变体，能稳定每个可稳定实例，因此是最大稳定的。
英文摘要
We study stochastic dynamic matching on hypergraphs: items of finitely many classes arrive over time and are removed in multisets by activating hyperedges. We characterize stabilizability, the existence of a matching policy under which the queue process is positive recurrent, in terms of the arrival rates and the incidence matrix alone: (G, $λ$) is stabilizable if and only if the conservation equation A$μ$ = $λ$ admits a nonnegative solution whose support induces a surjective submatrix, equivalently $λ$ lies in the interior of the cone generated by the hyperedges. This extends a characterization known for simple graphs (non-bipartiteness together with the independent-set inequalities) to arbitrary hyperedges, allowing multiplicities and mono-edges, and, unlike the constant-regret theory, needs no general-position assumption. Sufficiency is constructive: a single $λ$-oblivious policy, Virtual-Queue Match-the-Longest (VQML), a rewardless variant of the Extended Greedy Primal-Dual policy of Nazari and Stolyar, stabilizes every stabilizable instance and is therefore maximally stable. The sufficiency proof requires the positive recurrence of the signed virtual queue underlying VQML; previous analyses invoke this property but, to our knowledge, do not prove it, and supplying it is a second contribution.
