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- W1513524375 abstract "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." @default.
- W1513524375 created "2016-06-24" @default.
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- W1513524375 date "2013-12-18" @default.
- W1513524375 modified "2023-09-23" @default.
- W1513524375 title "A statistical view on exchanges in Quickselect" @default.
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- W1513524375 doi "https://doi.org/10.1137/1.9781611973204.4" @default.
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