TIGHT COMPLEXITY BOUNDS FOR PARALLEL COMPARISON SORTING.

Noga Alon; Yossi Azar; Uzi Vishkin

doi:10.1109/sfcs.1986.57

TIGHT COMPLEXITY BOUNDS FOR PARALLEL COMPARISON SORTING.

Noga Alon, Yossi Azar, Uzi Vishkin

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

12 Scopus citations

Abstract

The time complexity of sorting n elements using p greater than equivalent to n processors on L. G. Valiant's (1975) parallel comparison tree model is considered. It is shown that this time complexity is THETA (log n/log(1 plus p/n)). For every fixed time k it is shown that OMEGA (n**1** plus **1 **/ **k ) comparisons are required and that there exists a randomized algorithm for comparison sort in time k with an expected number of O(n**1** plus **1 **k comparisons. This implies that for every fixed k, any deterministic comparison sort algorithm must be asymptotically worse than this randomized algorithm. It is shown that 'approximate sorting' in time 1 requires asymptotically more than n log n processors.

Original language	English (US)
Title of host publication	Annual Symposium on Foundations of Computer Science (Proceedings)
Publisher	IEEE
Pages	502-510
Number of pages	9
ISBN (Print)	0818607408, 9780818607400
DOIs	https://doi.org/10.1109/sfcs.1986.57
State	Published - 1986
Externally published	Yes

Publication series

Name	Annual Symposium on Foundations of Computer Science (Proceedings)
ISSN (Print)	0272-5428

All Science Journal Classification (ASJC) codes

Hardware and Architecture

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10.1109/sfcs.1986.57

Cite this

@inproceedings{ea6c7c7d4cea4b339fa61f56f404f8fa,

title = "TIGHT COMPLEXITY BOUNDS FOR PARALLEL COMPARISON SORTING.",

abstract = "The time complexity of sorting n elements using p greater than equivalent to n processors on L. G. Valiant's (1975) parallel comparison tree model is considered. It is shown that this time complexity is THETA (log n/log(1 plus p/n)). For every fixed time k it is shown that OMEGA (n**1** plus **1 **/ **k ) comparisons are required and that there exists a randomized algorithm for comparison sort in time k with an expected number of O(n**1** plus **1 **k comparisons. This implies that for every fixed k, any deterministic comparison sort algorithm must be asymptotically worse than this randomized algorithm. It is shown that 'approximate sorting' in time 1 requires asymptotically more than n log n processors.",

author = "Noga Alon and Yossi Azar and Uzi Vishkin",

year = "1986",

doi = "10.1109/sfcs.1986.57",

language = "English (US)",

isbn = "0818607408",

series = "Annual Symposium on Foundations of Computer Science (Proceedings)",

publisher = "IEEE",

pages = "502--510",

booktitle = "Annual Symposium on Foundations of Computer Science (Proceedings)",

}

TY - GEN

T1 - TIGHT COMPLEXITY BOUNDS FOR PARALLEL COMPARISON SORTING.

AU - Alon, Noga

AU - Azar, Yossi

AU - Vishkin, Uzi

PY - 1986

Y1 - 1986

N2 - The time complexity of sorting n elements using p greater than equivalent to n processors on L. G. Valiant's (1975) parallel comparison tree model is considered. It is shown that this time complexity is THETA (log n/log(1 plus p/n)). For every fixed time k it is shown that OMEGA (n**1** plus **1 **/ **k ) comparisons are required and that there exists a randomized algorithm for comparison sort in time k with an expected number of O(n**1** plus **1 **k comparisons. This implies that for every fixed k, any deterministic comparison sort algorithm must be asymptotically worse than this randomized algorithm. It is shown that 'approximate sorting' in time 1 requires asymptotically more than n log n processors.

AB - The time complexity of sorting n elements using p greater than equivalent to n processors on L. G. Valiant's (1975) parallel comparison tree model is considered. It is shown that this time complexity is THETA (log n/log(1 plus p/n)). For every fixed time k it is shown that OMEGA (n**1** plus **1 **/ **k ) comparisons are required and that there exists a randomized algorithm for comparison sort in time k with an expected number of O(n**1** plus **1 **k comparisons. This implies that for every fixed k, any deterministic comparison sort algorithm must be asymptotically worse than this randomized algorithm. It is shown that 'approximate sorting' in time 1 requires asymptotically more than n log n processors.

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DO - 10.1109/sfcs.1986.57

M3 - Conference contribution

AN - SCOPUS:0022862838

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SN - 9780818607400

T3 - Annual Symposium on Foundations of Computer Science (Proceedings)

SP - 502

EP - 510

BT - Annual Symposium on Foundations of Computer Science (Proceedings)

PB - IEEE

ER -

TIGHT COMPLEXITY BOUNDS FOR PARALLEL COMPARISON SORTING.

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