article

Free access

A Permutation Network

Author:

Abraham WaksmanAuthors Info & Claims

Journal of the ACM (JACM), Volume 15, Issue 1

Pages 159 - 163

https://doi.org/10.1145/321439.321449

Published: 01 January 1968 Publication History

PDF eReader

Abstract

In this paper the construction of a switching network capable of n!-permutation of its n input terminals to its n output terminals is described. The building blocks for this network are binary cells capable of permuting their two input terminals to their two output terminals.

The number of cells used by the network is 〈n · log₂ n - n + 1〉 = Σⁿ _k=1 〈log₂ k〉. It could be argued that for such a network this number of cells is a lower bound, by noting that binary decision trees in the network can resolve individual terminal assignments only and not the partitioning of the permutation set itself which requires only 〈log₂ n!〉 = 〈Σⁿ _k=1 log₂ k〉 binary decisions.

An algorithm is also given for the setting of the binary cells in the network according to any specified permutation.

References

[1]

HALL, P. On representatives of subsets. J. London Math. Soe. 10 (1965), 26-30.

Google Scholar

[2]

BENES, V. E. MathemaTIcal Theory of connecting networks and Telephone Traffic. Academic Press New York, 1935.

Google Scholar

Cited By

View all

ANTONESCU MȘTEFAN G(2024)Multi-Function Scan Circuit for Assisting the Parallel Computational Map PatternRomanian Journal of Information Science and Technology10.59277/ROMJIST.2024.1.012024:1(3-20)Online publication date: 26-Mar-2024
https://doi.org/10.59277/ROMJIST.2024.1.01
Etzion T(2024)Interconnection networksSequences and the de Bruijn Graph10.1016/B978-0-44-313517-0.00018-4(405-457)Online publication date: 2024
https://doi.org/10.1016/B978-0-44-313517-0.00018-4
Ohta S(2023)Necessary Conditions and Empirical Observations for Rearrangeable Banyan-Type NetworksWSEAS TRANSACTIONS ON CIRCUITS AND SYSTEMS10.37394/23201.2023.22.2122(180-194)Online publication date: 31-Dec-2023
https://doi.org/10.37394/23201.2023.22.21
Show More Cited By

Index Terms

A Permutation Network

Recommendations

Permutation tableaux and permutation patterns

In this paper we introduce and study a class of tableaux which we call permutation tableaux; these tableaux are naturally in bijection with permutations, and they are a distinguished subset of the -diagrams of Alex Postnikov [A. Postnikov, Webs in ...
On the sign-imbalance of permutation tableaux

Permutation tableaux were introduced by Steingrmsson and Williams. Corteel and Kim defined the sign of a permutation tableau in terms of the number of unrestricted columns. The sign-imbalance of permutation tableaux of length n is the sum of signs over ...
The sorting index and permutation codes

In the combinatorial study of the coefficients of a bivariate polynomial that generalizes both the length and the reflection length generating functions for finite Coxeter groups, Petersen introduced a new Mahonian statistic sor, called the sorting ...

Comments

Information & Contributors

Information

Published In

Journal of the ACM Volume 15, Issue 1

Jan. 1968

163 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321439

Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 January 1968

Published in JACM Volume 15, Issue 1

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

372
Total Citations
View Citations
3,185
Total Downloads

Downloads (Last 12 months)554
Downloads (Last 6 weeks)53

Reflects downloads up to 27 Jul 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

ANTONESCU MȘTEFAN G(2024)Multi-Function Scan Circuit for Assisting the Parallel Computational Map PatternRomanian Journal of Information Science and Technology10.59277/ROMJIST.2024.1.012024:1(3-20)Online publication date: 26-Mar-2024
https://doi.org/10.59277/ROMJIST.2024.1.01
Etzion T(2024)Interconnection networksSequences and the de Bruijn Graph10.1016/B978-0-44-313517-0.00018-4(405-457)Online publication date: 2024
https://doi.org/10.1016/B978-0-44-313517-0.00018-4
Ohta S(2023)Necessary Conditions and Empirical Observations for Rearrangeable Banyan-Type NetworksWSEAS TRANSACTIONS ON CIRCUITS AND SYSTEMS10.37394/23201.2023.22.2122(180-194)Online publication date: 31-Dec-2023
https://doi.org/10.37394/23201.2023.22.21
Ivaniuk AShamyna A(2023)Physically non-cloneable arbiter -type function with non-linear path pairs«System analysis and applied information science»10.21122/2309-4923-2023-1-54-62(54-62)Online publication date: 2-Aug-2023
https://doi.org/10.21122/2309-4923-2023-1-54-62
Jin YHua FChen YHayes AZhang CZhang EAamodt TSwift MJerger N(2023)Exploiting the Regular Structure of Modern Quantum Architectures for Compiling and Optimizing Programs with Permutable OperatorsProceedings of the 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 410.1145/3623278.3624751(108-124)Online publication date: 25-Mar-2023
https://dl.acm.org/doi/10.1145/3623278.3624751
Jiang KChait-Roth DDeStefano ZWalfish MWies T(2023)Less is more: refinement proofs for probabilistic proofs2023 IEEE Symposium on Security and Privacy (SP)10.1109/SP46215.2023.10179393(1112-1129)Online publication date: May-2023
https://doi.org/10.1109/SP46215.2023.10179393
Zhang MZhang Y(2023)Arbitrary-size permutation networks using arbitrary-radix switchesTheoretical Computer Science10.1016/j.tcs.2023.113939962(113939)Online publication date: Jun-2023
https://doi.org/10.1016/j.tcs.2023.113939
Belorgey MCarpov SDeforth KJetchev DSae-Tang AVuille MGama NKatz JLeontiadis IMohammadi M(2023)Manticore: A Framework for Efficient Multiparty Computation Supporting Real Number and Boolean ArithmeticJournal of Cryptology10.1007/s00145-023-09464-436:3Online publication date: 11-Jul-2023
https://dl.acm.org/doi/10.1007/s00145-023-09464-4
Jia HLi X(2023)PFE: Linear Active Security, Double-Shuffle Proofs, and Low-Complexity CommunicationInformation Security and Cryptology10.1007/978-981-97-0942-7_12(227-252)Online publication date: 9-Dec-2023
https://dl.acm.org/doi/10.1007/978-981-97-0942-7_12
Xu YJia HLi XLi QBao YHou X(2023)Constant-Round Multiparty Private Function Evaluation with (Quasi-)Linear ComplexitiesApplied Cryptography and Network Security10.1007/978-3-031-33491-7_5(115-142)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-33491-7_5
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

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

Permutation tableaux and permutation patterns

On the sign-imbalance of permutation tableaux

The sorting index and permutation codes

Comments

Information

Published In

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations