Probabilistic integer sorting

Authors:
Alexandros V. Gerbessiotis;Constantinos J. Siniolakis
Affiliations:
CS Department, New Jersey Institute of Technology, Newark, NJ;The American College of Greece, 6 Gravias St., Athens 15342, Greece
Venue:
Information Processing Letters
Year:
2004

Citing 7
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Abstract

We introduce a probabilistic sequential algorithm for stable sorting n uniformly distributed keys in an arbitrary range. The algorithm runs in linear time and sorts all but a very small fraction 2-Ω(n) of the input sequences; the best previously known bound was 2-Ω(n/(lgn lg lgn)). An EREW PRAM extension of this sequential algorithm sorts in O((n/p + lg p)lg n/lg(n/p + lg n)) time using p ≤ n processors under the same probabilistic conditions. For a CRCW PRAM we improve upon the probabilistic bound of 2-Ω(n/(lg n lg lg n)) obtained by Rajasekaran and Sen to derive a 2-Ω(n lg lg n/lg n) bound. Additionally, we present experimental results for the sequential algorithm that establish the practicality of our method.