article

Free access

Topological sorting of large networks

Author:

A. B. KahnAuthors Info & Claims

Communications of the ACM, Volume 5, Issue 11

Pages 558 - 562

https://doi.org/10.1145/368996.369025

Published: 01 November 1962 Publication History

PDF eReader

Abstract

Topological Sorting is a procedure required for many problems involving analysis of networks. An example of one such problem is PERT. The present paper presents a very general method for obtaining topological order. It permits treatment of larger networks than can be handled on present procedures and achieves this with greater efficiency. Although the procedure can be adapted to any machine, it is discussed in terms of the 7090. A PERT network of 30,000 activities can be ordered in less than one hour of machine time.

The method was developed as a byproduct of procedure needed by Westinghouse, Baltimore. It has not been programmed and at present there are no plans to implement it. In regard to the techniques described, Westinghouse's present and anticipated needs are completely served by the Lockheed program, which is in current use.

References

[1]

Anonymous (1958), Summary Report, Phases 1 and 2, Program Evaluation Research Task. U. S. Government Printing Office, Washington, D.C.

Google Scholar

[2]

D. J. LASSER (1961), Topological ordering of a list of randomlynumbered elements of a network. Comm. ACM 4, 12 (1961).

Digital Library

Google Scholar

Cited By

View all

Li TDahleh M(2024)Automation of Strategic Data Prioritization in System Model CalibrationINFORMS Journal on Computing10.1287/ijoc.2022.012836:1(163-184)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1287/ijoc.2022.0128
Jiang H(2024)Qubit Recycling RevisitedProceedings of the ACM on Programming Languages10.1145/36564288:PLDI(1264-1287)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656428
Li NZhang MLi JAdepu SKang EJin Z(2024)A Game-Theoretical Self-Adaptation Framework for Securing Software-Intensive SystemsACM Transactions on Autonomous and Adaptive Systems10.1145/365294919:2(1-49)Online publication date: 20-Apr-2024
https://dl.acm.org/doi/10.1145/3652949
Show More Cited By

Recommendations

Sorting networks: To the end and back again
Abstract
New properties of the front and back ends of sorting networks are studied, illustrating their utility when searching for bounds on optimal networks. Search focuses first on the “out-sides” of the network and then on the inner part. ...
Highlights
- Faster sorting networks for 17, 19, and 20 inputs.
- 10 parallel steps are ...
Read More
Optimal-depth sorting networks

We prove depth optimality of sorting networks from "The Art of Computer Programming".Sorting networks posses symmetry that can be used to generate a few representatives.These representatives can be efficiently encoded using regular expressions.We ...
Read More
Reactive sorting networks
REBLS 2020: Proceedings of the 7th ACM SIGPLAN International Workshop on Reactive and Event-Based Languages and Systems

Sorting is a central problem in computer science and one of the key components of many applications. To the best of our knowledge, no reactive programming implementation of sorting algorithms has ever been presented.

In this paper we present reactive ...
Read More

Comments

Information & Contributors

Information

Published In

Communications of the ACM Volume 5, Issue 11

Nov. 1962

178 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/368996

Editor:
C. C. Gotlieb
Univ. of Toronto, Toronto, Canada

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 November 1962

Published in CACM Volume 5, Issue 11

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

504
Total Citations
View Citations
4,330
Total Downloads

Downloads (Last 12 months)872
Downloads (Last 6 weeks)149

Other Metrics

View Author Metrics

Citations

Cited By

View all

Li TDahleh M(2024)Automation of Strategic Data Prioritization in System Model CalibrationINFORMS Journal on Computing10.1287/ijoc.2022.012836:1(163-184)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1287/ijoc.2022.0128
Jiang H(2024)Qubit Recycling RevisitedProceedings of the ACM on Programming Languages10.1145/36564288:PLDI(1264-1287)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656428
Li NZhang MLi JAdepu SKang EJin Z(2024)A Game-Theoretical Self-Adaptation Framework for Securing Software-Intensive SystemsACM Transactions on Autonomous and Adaptive Systems10.1145/365294919:2(1-49)Online publication date: 20-Apr-2024
https://dl.acm.org/doi/10.1145/3652949
Sağlam TBrödel MSchmid LHahner SRoychoudhury APaiva AAbreu RStorey M(2024)Detecting Automatic Software Plagiarism via Token Sequence NormalizationProceedings of the IEEE/ACM 46th International Conference on Software Engineering10.1145/3597503.3639192(1-13)Online publication date: 20-May-2024
https://dl.acm.org/doi/10.1145/3597503.3639192
Dey TLipiński MMrozek MSlechta R(2024)Computing Connection Matrices via Persistence-Like ReductionsSIAM Journal on Applied Dynamical Systems10.1137/23M156246923:1(81-97)Online publication date: 4-Jan-2024
https://doi.org/10.1137/23M1562469
Cao KWeng J(2024)REPFS: Reliability-Ensured Personalized Function Scheduling in Sustainable Serverless Edge ComputingIEEE Transactions on Sustainable Computing10.1109/TSUSC.2023.33366919:3(494-511)Online publication date: May-2024
https://doi.org/10.1109/TSUSC.2023.3336691
Chen KAstolfi A(2024)Active Nodes of Network Systems With Sum-Type Dissipation InequalitiesIEEE Transactions on Automatic Control10.1109/TAC.2023.334487169:6(3896-3911)Online publication date: Jun-2024
https://doi.org/10.1109/TAC.2023.3344871
Hong CYuan MZhang MWang XZhang CWang JPan GTang H(2024)SPAIC: A Spike-Based Artificial Intelligence Computing FrameworkIEEE Computational Intelligence Magazine10.1109/MCI.2023.332784219:1(51-65)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1109/MCI.2023.3327842
Min JKim WPaek JGovindan R(2024)Effective Routing and Scheduling Strategies for Fault-Tolerant Time-Sensitive NetworkingIEEE Internet of Things Journal10.1109/JIOT.2023.332862611:6(11008-11020)Online publication date: 15-Mar-2024
https://doi.org/10.1109/JIOT.2023.3328626
Lin ZMiao YXu GLi CSaarikivi OMaleki SYang F(2024)Tessel: Boosting Distributed Execution of Large DNN Models via Flexible Schedule Search2024 IEEE International Symposium on High-Performance Computer Architecture (HPCA)10.1109/HPCA57654.2024.00067(803-816)Online publication date: 2-Mar-2024
https://doi.org/10.1109/HPCA57654.2024.00067
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

Recommendations

Sorting networks: To the end and back again

Optimal-depth sorting networks

Reactive sorting networks

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