Topological sorting of large networks
Open accessAbstract
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.
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Insertions are countered via subsequence removal, and reordering is negated by topological sorting.
“(a) Insertions are countered via subsequence removal.(b) Reordering is negated by topological sorting [19].”
From Detecting Automatic Software Plagiarism via Token Sequence Normalization (2024) · cites this paper as [19]
Topological sorting of the TNG counters attempts to re-order the token sequence.
“Next, we use topological sorting [19] to generate a normalized token sequence.This counters attempts to re-order the token sequence.”
From Detecting Automatic Software Plagiarism via Token Sequence Normalization (2024) · cites this paper as [19]
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Detecting Automatic Software Plagiarism via Token Sequence Normalization
Sağlam, T., Brödel, M., Schmid, L., & Hahner, S. (2024) · Proceedings of the IEEE/ACM 46th International Conference on Software Engineering · doi:10.1145/3597503.3639192 · Cited by 9 · see citing works
Scaling Large Language Model-based Multi-Agent Collaboration
Qian, C., Xie, Z., Wang, Y., Liu, W., Zhu, K., Xia, H., Dang, Y., Du, Z., Chen, W., Yang, C., et al. (2024) · arXiv · doi:10.48550/arxiv.2406.07155 · Cited by 8 · see citing works
“Topo-logical sorting is implemented via Kahn’s algo-rithm (Kahn, 1962).”
- Authors
- Kahn, A. B.
- Affiliations
- Westinghouse Electric (United States) (US)
- Corresponding author
- Kahn, A. B.
- Venue
- Communications of the ACM
- Published
- 1962-11
- Volume
- 5
- Issue
- 11
- Pages
- 558-562
- ISSN
- 0001-0782 (ISSN-L)
- 1557-7317
- OpenAlex
- W2063123613
- Cited by
- 769
- References
- 0
- Citations by year
- 2026: 55 · 2025: 51 · 2024: 56 · 2023: 53 · 2022: 60 · 2021: 61 · 2020: 63 · 2019: 42 · 2018: 62 · 2017: 31 · 2016: 37 · 2015: 27 · 2014: 32 · 2013: 23 · 2012: 29
- FWCI
- 1.11
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Communications of the ACM (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Graph Theory and Algorithms
- Social Sciences › Decision Sciences › Management Science and Operations Research › Resource-Constrained Project Scheduling
- Keywords
- topological sorting, large-scale networks, PERT networks, topological order, network analysis, computational efficiency, IBM 7090, project scheduling
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