Highly Influenced

5 Excerpts

- Published 2000 in ArXiv

Using Fourier analysis, we prove that the limiting distribution of the standardized random number of comparisons used by Quicksort to sort an array of n numbers has an everywhere positive and infinitely differentiable density f , and that each derivative f (k) enjoys superpolynomial decay at ±∞. In particular, each f (k) is bounded. Our method is sufficiently computational to prove, for example, that f is bounded by 16. AMS 2000 subject classifications. Primary 68W40; secondary 68P10, 60E05, 60E10.

@article{Fill2000SmoothnessAD,
title={Smoothness and decay properties of the limiting Quicksort density function},
author={James Allen Fill and Svante Janson},
journal={CoRR},
year={2000},
volume={math.PR/0005235}
}