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Cost-minimal trees in directed acyclic graphs

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Summary

A number of examples are given where one seeks a minimal-cost tree to span a given subset of the nodes of a connected, directed, acyclic graph (we call such a graph monotonic). Some of these examples require an algorithm to transform the problem into the form of a minimization problem in a monotonic graph; this algorithm is also given. Finally, an implicit enumeration algorithm is presented for finding the cost-minimal tree of the graph, which spans the designated subset of the nodes, and some computational results are given.

Zusammenfassung

Es werden Beispiele aufgezeigt, bei denen ein kostenminimaler Baum gesucht wird, der eine gegebene Untermenge von Knoten in einem verbundenen, gerichteten und azyklischen Graphen aufspannt. Ein solcher Graph wird hier als monotoner Graph bezeichnet. Einige dieser Beispiele erfordern einen Algorithmus, der das gegebene Problem in eine Minimierungsaufgabe in einem monotonen Graphen überträgt. Dieser Algorithmus zur Konstruktion des Graphen wird formuliert. Schließlich wird ein spezialisiertes implizites Enumerationsverfahren vorgestellt, das den kostenminimalen Baum zu der gegebenen Untermenge von Knoten in dem vorliegenden monotonen Graphen konstruiert. Rechenerfahrungen bilden den Abschluß.

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Authors and Affiliations

  1. Fachbereich Wirtschaftswissenschaften, Universität des Saarlandes, 66 Saarbrücken, W-Germany

    L. Nastansky

  2. Départment d'informatique, Université de Montréal, C. P. 6128, Montréal 101, P. Q., Canada

    S. M. Selkow Ph. D. &  N. F. Stewart Ph. D.

Authors
  1. L. Nastansky
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  2. S. M. Selkow Ph. D.
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  3. N. F. Stewart Ph. D.
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Nastansky, L., Selkow, S.M. & Stewart, N.F. Cost-minimal trees in directed acyclic graphs. Zeitschrift für Operations Research 18, 59–67 (1974). https://doi.org/10.1007/BF01949715

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  • DOI: https://doi.org/10.1007/BF01949715

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