发表机构
Univ. Paris-Saclay, UVSQ; INRIA（巴黎萨克雷大学，凡尔赛大学; 法国国家信息与自动化研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明在自同构转移一致性条件下，任意具有非平凡自同构群的相容图对应的马尔可夫链可强聚合，并扩展到非贪婪匹配，以奇环为例验证，深化了随机匹配模型的可 lump 性理论。
AI 中文摘要
我们将强聚合的分析扩展到一般的相容图，重点关注物品数量而非位置，并探索广义的贪婪匹配策略。我们证明，在基于自同构的转移一致性条件下，对于具有非平凡自同构群的任意图，相关的马尔可夫链是强可聚合的。此外，我们将分析扩展到非贪婪匹配策略，区分相容物品在同一状态内可以共存和不能共存的场景。这一结果通过一个具有丰富自同构结构的简单相容图——奇环——加以说明。对于所有场景，我们研究了所得马尔可夫链的强聚合性质。这项工作增强了随机匹配模型中可 lumpability（可 lump 性）的理论理解，并为分析复杂图结构提供了基础。
英文摘要
We extend the analysis of strong aggregation to general compatibility graphs, focusing on item counts rather than positions, and exploring generalized greedy matching disciplines. We prove that under a condition of automorphism-based transition consistency, the associated Markov chain is strongly aggregable for an arbitrary graph with a non-trivial automorphism group. Furthermore, we extend our analysis to non-greedy matching disciplines, distinguishing scenarios where compatible items can or cannot coexist within the same state. This result is illustrated with a simple compatibility graph with a rich automorphism structure: the odd rings. For all scenarios, we investigate the strong aggregation properties of the resulting Markov chains. This work enhances the theoretical understanding of lumpability in stochastic matching models and provides a foundation for analyzing complex graph structures.
