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Computational experiences with some transitive closure algorithms

Rechnererfahrungen mit einigen Algorithmen für die transitive Hülle eines gerichteten Graphen

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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.

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References

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

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    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).

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

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

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

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Keywords

  • Computational Mathematic
  • Computational Experience
  • Transitive Closure
  • Closure Algorithm
  • Transitive Closure Algorithm