research-article

Probabilistic Parallel Algorithms for Sorting and Selection

Author:

Rüdiger ReischukAuthors Info & Claims

SIAM Journal on Computing, Volume 14, Issue 2

Pages 396 - 409

https://doi.org/10.1137/0214030

Published: 01 May 1985 Publication History

Abstract

Probabilistic parallel algorithms are described to sort n keys and to select the k-smallest element among them. For each problem we construct a probabilistic parallel decision tree. The tree for selection finishes with high probability in constant time and the sorting tree in time $O(\log n)$. The same time bound for sorting can also be achieved by a probabilistic parallel machine consisting of n RAMs, each with small private memory, and a common memory of size $O(n)$. These algorithms meet the information theoretic lower bounds.

References

[1]

A. Aho, J. Hopcroft, J. Ullman, The design and analysis of computer algorithms, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975x+470

Google Scholar

[2]

R. Floyd, R. Rivest, Expected time bounds for selection, Comm. ACM, 18 (1975), 165–172

Digital Library

Google Scholar

[3]

P. Häggkvist, P. Hell, Parallel sorting with constant time for comparisons, SIAM J. Comput., 10 (1981), 465–472

Digital Library

Google Scholar

[4]

Franco P. Preparata, New parallel-sorting schemes, IEEE Trans. Comput., 27 (1978), 669–673

Digital Library

Google Scholar

[5]

Leslie G. Valiant, Parallelism in comparison problems, SIAM J. Comput., 4 (1975), 348–355

Digital Library

Google Scholar

Cited By

View all

Goodrich MJacob RAgrawal KShun J(2023)Optimal Parallel Sorting with Comparison ErrorsProceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3558481.3591093(355-365)Online publication date: 17-Jun-2023
https://dl.acm.org/doi/10.1145/3558481.3591093
Gerbessiotis ASiniolakis C(1997)A Randomized Sorting Algorithm on the BSP modelProceedings of the 11th International Symposium on Parallel Processing10.5555/645607.661675(293-297)Online publication date: 1-Apr-1997
https://dl.acm.org/doi/10.5555/645607.661675
Gibbons PMatias YRamachandran VSnyder LLeiserson C(1994)Efficient low-contention parallel algorithmsProceedings of the sixth annual ACM symposium on Parallel algorithms and architectures10.1145/181014.181382(236-247)Online publication date: 1-Aug-1994
https://dl.acm.org/doi/10.1145/181014.181382

Index Terms

Probabilistic Parallel Algorithms for Sorting and Selection

Index terms have been assigned to the content through auto-classification.

Recommendations

Efficient in-place sorting algorithms using feasible parallel machine models
ISPAN '96: Proceedings of the 1996 International Symposium on Parallel Architectures, Algorithms and Networks

We present a simple and general parallel sorting scheme, ZZ-sort, which can be used to derive a class of efficient in-place sorting algorithms on realistic parallel machine models. We prove a tight bound for the worst case performance of ZZ-sort. We ...
Parallel Quicksort Using Fetch-And-Add

A parallelization of the Quicksort algorithm that is suitable for execution on a shared memory multiprocessor with an efficient implementation of the fetch-and-add operation is presented. The partitioning phase of Quicksort, which has been considered a ...
An Efficient General In-Place Parallel Sorting Scheme

We present a simple and general parallel sorting scheme, ZZ-sort, which can be used to derive a class of efficient in-place sorting algorithms on realistic parallel machine models. We prove a tight bound for the worst case performance of ZZ-sort. We ...

Comments

Information & Contributors

Information

Published In

SIAM Journal on Computing Volume 14, Issue 2

May 1985

247 pages

ISSN:0097-5397

DOI:10.1137/smjcat.1985.14.issue-2

Issue’s Table of Contents

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 May 1985

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

3
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 11 Aug 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Goodrich MJacob RAgrawal KShun J(2023)Optimal Parallel Sorting with Comparison ErrorsProceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3558481.3591093(355-365)Online publication date: 17-Jun-2023
https://dl.acm.org/doi/10.1145/3558481.3591093
Gerbessiotis ASiniolakis C(1997)A Randomized Sorting Algorithm on the BSP modelProceedings of the 11th International Symposium on Parallel Processing10.5555/645607.661675(293-297)Online publication date: 1-Apr-1997
https://dl.acm.org/doi/10.5555/645607.661675
Gibbons PMatias YRamachandran VSnyder LLeiserson C(1994)Efficient low-contention parallel algorithmsProceedings of the sixth annual ACM symposium on Parallel algorithms and architectures10.1145/181014.181382(236-247)Online publication date: 1-Aug-1994
https://dl.acm.org/doi/10.1145/181014.181382

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Abstract

References

Cited By

Index Terms

Recommendations

Efficient in-place sorting algorithms using feasible parallel machine models

Parallel Quicksort Using Fetch-And-Add

An Efficient General In-Place Parallel Sorting Scheme

Comments

Information

Published In

Publisher

Publication History

Author Tags

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations