A characterization of the set of fixed points of the Quicksort transformation
Probability
2007-05-23 v1 Data Structures and Algorithms
Abstract
The limiting distribution \mu of the normalized number of key comparisons required by the Quicksort sorting algorithm is known to be the unique fixed point of a certain distributional transformation T -- unique, that is, subject to the constraints of zero mean and finite variance. We show that a distribution is a fixed point of T if and only if it is the convolution of \mu with a Cauchy distribution of arbitrary center and scale. In particular, therefore, \mu is the unique fixed point of T having zero mean.
Keywords
Cite
@article{arxiv.math/0005236,
title = {A characterization of the set of fixed points of the Quicksort transformation},
author = {James Allen Fill and Svante Janson},
journal= {arXiv preprint arXiv:math/0005236},
year = {2007}
}
Comments
9 pages. See also http://www.mts.jhu.edu/~fill/ and http://www.math.uu.se/~svante/papers . Submitted for publication in May,2000