一种用于偏序时间一致性检查的快速算法
A Fast Algorithm for Consistency Checking Partially Ordered Time
AI总结：
本文针对偏序时间点代数的网络一致性问题，提出一种运行时间为 $O^*((0.26n)^n)$ 的快速算法，通过精细枚举类全序结构并贪婪扩展，显著优于此前 $O^*((0.368n)^n)$ 的算法。
摘要：
偏序时间模型自然出现在智能体或进程无法彼此完美通信的应用中，并可追溯到 Lamport 的开创性工作。本文考虑的问题是：判断一个（可能不完整的）事件系统描述是否一致，即偏序时间点代数（POT）的网络一致性问题。虽然该问题的经典复杂度已完全确定，但关于 POT 的细粒度复杂度所知甚少，只知道它可以通过枚举有序划分在 $O^*((0.368n)^n)$ 时间内求解。我们构造了一个快得多的算法，其运行时间上界为 $O^*((0.26n)^n)$。这是通过对类似于全序的结构进行精细枚举实现的，然后贪婪地将这些结构扩展为解。虽然类似的思想早期已在相关问题中探索过，但结果表明，对 POT 的分析并非平凡，需要重要的新思想。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
