Partially ordered models of time occur naturally in applications where agents or processes cannot perfectly communicate with each other, and can be traced back to the seminal work of Lamport. In this paper we consider the problem of deciding if a (likely incomplete) description of a system of events is consistent, the network consistency problem for the point algebra of partially ordered time (POT). While the classical complexity of this problem has been fully settled, comparably little is known of the fine-grained complexity of POT except that it can be solved in $O^*((0.368n)^n)$ time by enumerating ordered partitions. We construct a much faster algorithm with a run-time bounded by $O^*((0.26n)^n)$. This is achieved by a sophisticated enumeration of structures similar to total orders, which are then greedily expanded toward a solution. While similar ideas have been explored earlier for related problems it turns out that the analysis for POT is non-trivial and requires significant new ideas.

翻译：部分有序时间模型在代理或进程无法完美通信的应用中自然出现，可追溯至Lamport的开创性工作。本文研究事件系统（可能不完整）描述的一致性判定问题，即部分有序时间（POT）点代数上的网络一致性检验问题。虽然该问题的经典复杂度已完全明确，但其细粒度复杂度除可通过枚举有序划分在 $O^*((0.368n)^n)$ 时间内求解外鲜为人知。我们构建了一个更快的算法，其运行时间上界为 $O^*((0.26n)^n)$。这是通过精巧枚举类似全序的结构，随后对其贪心扩展至解而实现的。尽管类似思想此前已被用于探索相关问题，但POT的分析具有非平凡性，需要重要的新思路。