Skip to main content
Log in

Computational experiences with some transitive closure algorithms

Rechnererfahrungen mit einigen Algorithmen für die transitive Hülle eines gerichteten Graphen

  • Published:
Computing Aims and scope Submit manuscript

Abstract

The paper contains results of computational experiences with the following algorithms for finding the transitive closure of a digraph: (i) Warshall's algorithm [17], (ii) Purdom's algorithm [13], (iii) the modification of Yen's algorithm [14], and (iv) the new algorithms for finding the transitive closure [3, 4]. The tested digraphs were generated at random. The enclosed references contain all papers known to the authors concerning transitive closure algorithms.

Zusammenfassung

Folgende Algorithmen wurden untersucht: 1. Warshall's Algorithm [17], 2. Purdom's Algorithm [13], 3. der modifizierte Algorithmus von Yen [14], 4. der Algorithmus von Dzikiewicz [3, 4]. Die getesteten Digraphen wurden durch einen Zufallsgenerator erzeugt. Das Literaturverzeichnis enthält alle Veröffentlichungen über Algorithmen zur Bildung der transitiven Hülle, welche den Verfassern bekannt sind.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aho, A. V., Garey, M. R., Ullman, J. D.: The transitive reduction of directed graph. SIAM J. Comput.1, 131–137 (1972).

    Article  Google Scholar 

  2. Arlazarow, V. L., Dinic, E. A. Kronrod, M. A., Faradzehev, I. A.: On economical construction of the transitive closure of an oriented graph. DAN SSSR194, 487–488 (1970).

    Google Scholar 

  3. Dzikiewicz, J.: Transitive closure algorithms. M.S. Dissertation, Dept. of Numerical Methods, University of Wroclaw, Wroclaw 1974.

    Google Scholar 

  4. Dzikiewicz, J.: An algorithm for finding the transitive closure of a digraph. Computing15, 75–79 (1975).

    Google Scholar 

  5. Faradzehev, I. A.: Effective algorithms for solving some problems of directed graph theory. Ž. Vyčisl. Mat. i Mat. Fiz.10, 1049–1054 (1970).

    Google Scholar 

  6. Fischer, M. J., Meyer, A. R.: Boolean matrix multiplication and transitive closure. IEEE Conf. Record of the Twelfth Annual Symp. on Switching and Automata Theory1971, 129–131.

  7. Floyd, R. W.: Algorithm 96: Ancestor. Comm. ACM5, 344 (1962).

    Article  Google Scholar 

  8. Furman, M. E.: Application of a method of fast multiplication of matrices in the problem of finding the transitive closure of a graph. DAN SSSR194, 524 (1970).

    Google Scholar 

  9. Harary, F., Norman, R. Z., Cartwright, D.: Structural models: An introduction to the theory of directed graphs. New York: Wiley. 1965.

    Google Scholar 

  10. Martynjuk, V. V.: On economical construction of the transitive closure of a binary relation. Ž. Vyčisl. Mat. i Mat. Fiz.2, 723–725 (1962).

    Google Scholar 

  11. Munro, J. I.: Efficient determination of the transitive closure of a directed graph. Information Processing Letters1, 56–58 (1971).

    Article  Google Scholar 

  12. O'Neil, P. E., O'Neil, E. J.: A fast expected time algorithm for Boolean matrix multiplication and transitive closure. Information and Control22, 132–138 (1973).

    Article  Google Scholar 

  13. Purdom, P.: A transitive closure algorithm. BIT10, 76–94 (1970).

    Article  Google Scholar 

  14. Sysło, M. M.: Transitive closure of a graph. Zastosow. Matem.14, 477–480 (1974).

    Google Scholar 

  15. Tarjan, R. E.: Depth, first search and linear graph algorithms. SIAM J. Comput.1, 146–160 (1972).

    Article  Google Scholar 

  16. Thorelli, L. E.: An algorithm for computing all paths in a graph. BIT6, 347–349 (1966).

    Article  Google Scholar 

  17. Warshall, S.: A theorem on Boolean matrices. Journ. ACM9, 11–12 (1962).

    Article  Google Scholar 

  18. Yen, J. Y.: Algorithms for finding all connectivities in directed and undirected networks. Preprint, 1973.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sysło, M.M., Dzikiewicz, J. Computational experiences with some transitive closure algorithms. Computing 15, 33–39 (1975). https://doi.org/10.1007/BF02252834

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02252834

Keywords

Navigation