A probabilistic analysis of the Floyd-Rivest expected time selection algorithm

Alexandros V. Gerbessiotis; Constantinos J. Siniolakis

doi:10.1080/00207160512331331048

A probabilistic analysis of the Floyd-Rivest expected time selection algorithm

Alexandros V. Gerbessiotis
, Constantinos J. Siniolakis

Computer Science

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We present a probabilistic analysis of the Floyd-Rivest expected time selection algorithm. In particular, we show that a refinement of the bootstrapped version of the Floyd-Rivest algorithm that determines the Cth order statistic by performing an expected n + C + O(n^1/2) comparisons can be made into a randomized algorithm that performs n + C + O(n^1/2 log^3/2 n) comparisons with probability at least 1 - 1/n ^ρ, for any constant ρ > 0.

Original language	English (US)
Pages (from-to)	509-519
Number of pages	11
Journal	International Journal of Computer Mathematics
Volume	82
Issue number	5
DOIs	https://doi.org/10.1080/00207160512331331048
State	Published - May 2005

All Science Journal Classification (ASJC) codes

Computer Science Applications
Computational Theory and Mathematics
Applied Mathematics

Keywords

Algorithms
Floyd-Rivest selection algorithm
Randomization
Selection

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10.1080/00207160512331331048

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abstract = "We present a probabilistic analysis of the Floyd-Rivest expected time selection algorithm. In particular, we show that a refinement of the bootstrapped version of the Floyd-Rivest algorithm that determines the Cth order statistic by performing an expected n + C + O(n1/2) comparisons can be made into a randomized algorithm that performs n + C + O(n1/2 log3/2 n) comparisons with probability at least 1 - 1/n ρ, for any constant ρ > 0.",

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AB - We present a probabilistic analysis of the Floyd-Rivest expected time selection algorithm. In particular, we show that a refinement of the bootstrapped version of the Floyd-Rivest algorithm that determines the Cth order statistic by performing an expected n + C + O(n1/2) comparisons can be made into a randomized algorithm that performs n + C + O(n1/2 log3/2 n) comparisons with probability at least 1 - 1/n ρ, for any constant ρ > 0.

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KW - Floyd-Rivest selection algorithm

KW - Randomization

KW - Selection

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ER -

A probabilistic analysis of the Floyd-Rivest expected time selection algorithm

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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