Some computations are based on structures of random partition. They take an n-size problem as input, then break this problem into sub-problems of randomized size, execute calculations on each sub-problems and combine results from these calculations at last. We propose a combinatorial method for analyzing such computations and prove that the averaged time complexity is in terms of Stirling numbers of the second kind. The result shows that the average time complexity is decreased about one order of magnitude compared to that of the original solution. We also show two application cases where random partition structures are applied to improve performance.

中文翻译：

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随机划分计算的平均时间复杂度

一些计算是基于随机分区的结构。他们将 n 大小的问题作为输入，然后将该问题分解为随机大小的子问题，对每个子问题执行计算并组合结果最后从这些计算中。我们提出了一种组合方法来分析此类计算，并证明平均时间复杂度是用第二类斯特林数表示的。结果表明，与原解相比，平均时间复杂度降低了约一个数量级。我们还展示了两个应用随机分区结构来提高性能的应用案例。