Quickselect中的交易所统计视图
A statistical view on exchanges in Quickselect
摘要：
在本文中，我们研究了Hoare的FIND算法（也称为快速选择）所需的密钥交换的数量时，操作的均匀分布的随机排列，并选择一个独立的均匀分布的秩。在正规化之后，我们给出了一个极限定理，其中极限定律是一个由递归分布方程表征的不灭性。为了使极限定理可用于统计方法和统计实验，我们提供了一个明确收敛速率在Kolmogorov-Smirnov度量，一个数值表的极限定律的分布函数和算法的精确模拟极限分布。我们还研究了极限定律的稠密性。本案例研究提供了一个程序，适用于其他成本措施，替代模型的排名选择和更平衡的选择主元，如中位数的$2t+1$版本的快速选择，以及进一步的变化的算法。
英文摘要：
In this paper we study the number of key exchanges required by Hoare's FIND algorithm (also called Quickselect) when operating on a uniformly distributed random permutation and selecting an independent uniformly distributed rank. After normalization we give a limit theorem where the limit law is a perpetuity characterized by a recursive distributional equation. To make the limit theorem usable for statistical methods and statistical experiments we provide an explicit rate of convergence in the Kolmogorov--Smirnov metric, a numerical table of the limit law's distribution function and an algorithm for exact simulation from the limit distribution. We also investigate the limit law's density. This case study provides a program applicable to other cost measures, alternative models for the rank selected and more balanced choices of the pivot element such as median-of-$2t+1$ versions of Quickselect as well as further variations of the algorithm.
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。
