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June 2011 Analysis of swaps in radix selection
Amr Elmasry, Hosam Mahmoud
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Adv. in Appl. Probab. 43(2): 524-544 (June 2011).

Abstract

Radix Sort is a sorting algorithm based on analyzing digital data. We study the number of swaps made by Radix Select (a one-sided version of Radix Sort) to find an element with a randomly selected rank. This kind of grand average provides a smoothing over all individual distributions for specific fixed-order statistics. We give an exact analysis for the grand mean and an asymptotic analysis for the grand variance, obtained by poissonization, the Mellin transform, and depoissonization. The digital data model considered is the Bernoulli(p). The distributions involved in the swaps experience a phase change between the biased cases (p ≠ ½) and the unbiased case (p = ½). In the biased cases, the grand distribution for the number of swaps (when suitably scaled) converges to that of a perpetuity built from a two-point distribution. The tool for this proof is contraction in the Wasserstein metric space, and identifying the limit as the fixed-point solution of a distributional equation. In the unbiased case the same scaling for the number of swaps gives a limiting constant in probability.

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Amr Elmasry. Hosam Mahmoud. "Analysis of swaps in radix selection." Adv. in Appl. Probab. 43 (2) 524 - 544, June 2011.

Information

Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1229.60012
MathSciNet: MR2848389

Subjects:
Primary: 60C05
Secondary: 60F05, 68P10

Rights: Copyright © 2011 Applied Probability Trust

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Vol.43 • No. 2 • June 2011
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