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An algorithm for finding a minimal equivalent graph of a strongly connected digraph

Ein Algorithmus, der zu einem stark zusammenhängenden Digraph einen äquivalenten kantenminimalen Digraph bestimmt

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Abstract

The paper presents a new branch and bound algorithm for removing the maximum number of edges from a strongly connected digraph without affecting its reachability properties.

A FORTRAN IV implementation is given.

The efficiency of the algorithm is analyzed through computational comparison with the methods of Moyles-Thompson and Hsu.

Zusammenfassung

Es wird ein neuer Branch-and-Bound-Algorithmus vorgestellt, der aus einem stark zusammenhängenden Digraphen eine maximale Anzahl von Kanten entfernt, ohne die Zusammenhangsverhältnisse zu verändern.

Eine FORTRAN IV Version des Algorithmus ist beigefügt.

Das Verhalten des Algorithmus wird durch Abschätzung der Komplexität und durch Vergleich mit den Algorithmen von Moyles-Thompson und Hsu verdeutlicht.

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References

  1. Hsu, H. T.: An Algorithm for Finding a Minimal Equivalent Graph of a Digraph. Journal of ACM22 (1975).

  2. Moyles, D. M., Thompson, G. L.: An Algorithm for Finding a Minimum Equivalent Graph of a Digraph. Journal of ACM16 (1969).

  3. Yen, J. Y.: Finding the Lengths of all Shortest Paths inN-Node Nonnegative Distance Complete Networks Using 1/2N 3 Additions andN 3 Comparisons. Journal of ACM19 (1972).

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Authors and Affiliations

  1. Istituto di Automatica, University of Bologna, Viale Risorgimento, 2, I-40136, Bologna, Italy

    S. Martello

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  1. S. Martello
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Martello, S. An algorithm for finding a minimal equivalent graph of a strongly connected digraph. Computing 21, 183–194 (1979). https://doi.org/10.1007/BF02253052

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  • DOI: https://doi.org/10.1007/BF02253052

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