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An adaptive and cost-optimal parallel algorithm for minimum spanning trees

Ein adaptiver und kostenoptimaler Parallel-Algorithmus für Minimalgerüste

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Abstract

A parallel algorithm is described for computing the minimum spanning tree of an undirected, connected and weighted graph withn vertices. We assume a shared-memory single-instruction-stream, multiple-data-stream model of computation which does not allow read or write conflicts. The algorithm is adaptive in the sense that it usesn 1−e processors and runs inO(n 1+e) time wheree lies between 0 and 1 and depends on the number of available processors. In view of the obvious Ω(n 2) lower bound on the number of operations required to compute a minimum spanning tree, the algorithm is also cost-optimal.

Zusammenfassung

Wir beschreiben einen Parallel-Algorithmus, der ein Minimalgerüst für einen ungerichteten, zusammenhängenden bewerteten Graphen mitn-Knoten ermittelt. Das zugrunde liegende Rechnermodell ist ein Mehrprozessorsystem mit gemeinsamem Speicher, das vielfachen Datentransfer erlaubt und von einer einzigen Zentraleinheit kontrolliert wird. Lese- oder Schreibkonflikte des Systems sollen ausgeschlossen sein. — Der Algorithmus paßt sich an die Zahl der verfügbaren Prozessoren an. Mitn 1−e-Prozessoren läuft er in der ZeitO(n 1+e), wobeie zwischen null und eins liegt. Der Algorithmus ist kostenoptimal, da die Berechnung des Minimalgerüsts Ω(n 2) Operationen benötigt.

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Authors and Affiliations

  1. Department of Computing and Information Science, Queen's University, Kingston, Ontario, Canada

    S. G. Akl

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  1. S. G. Akl
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Additional information

This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant NSERC-A3336 (Technical Report No. 85-164).

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Akl, S.G. An adaptive and cost-optimal parallel algorithm for minimum spanning trees. Computing 36, 271–277 (1986). https://doi.org/10.1007/BF02240073

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  • DOI: https://doi.org/10.1007/BF02240073

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