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

Byline: S. G. Akl (1) Keywords: B.3.2 [Memory Structures]: Design Styles -- shared memory; C.1.2 [Computer System Organization]: Multiple Data Stream Architectures (Multi-processors) -- single-instruction-stream, multiple-data-stream processors (SIMD); F.1.2 [Computation by Devices]: Modes of Comput... Full description

Journal Title: Computing 1986, Vol.36 (3), p.271-277
Main Author: AKL, S. G
Format: Electronic Article Electronic Article
Language: English
Subjects:
Publisher: Wien: Springer
ID: ISSN: 0010-485X
Link: http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=7942432
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recordid: cdi_gale_infotracacademiconefile_A153918049
title: An adaptive and cost-optimal parallel algorithm for minimum spanning trees
format: Article
creator:
  • AKL, S. G
subjects:
  • Algorithmics. Computability. Computer arithmetics
  • Algorithms
  • Analysis
  • Applied sciences
  • Computer science
  • control theory
  • systems
  • Exact sciences and technology
  • Theoretical computing
ispartof: Computing, 1986, Vol.36 (3), p.271-277
description: Byline: S. G. Akl (1) Keywords: B.3.2 [Memory Structures]: Design Styles -- shared memory; C.1.2 [Computer System Organization]: Multiple Data Stream Architectures (Multi-processors) -- single-instruction-stream, multiple-data-stream processors (SIMD); F.1.2 [Computation by Devices]: Modes of Computation -- parallelism; F.2.2, F.2.3 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems -- computations on discrete structures; Tradeoffs among Complexity Measures; G.2.2 [Discrete Mathematics]: Graph Theory -- graph algorithms, trees; Algorithms; Adaptive algorithm; cost-optimal algorithm; minimum spanning tree; parallel algorithm 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 .sup.1-e processors and runs inO(n .sup.1+e) time wheree lies between 0 and 1 and depends on the number of available processors. In view of the obvious [OMEGA](n .sup.2) lower bound on the number of operations required to compute a minimum spanning tree, the algorithm is also cost-optimal. (German): Wir beschreiben einen Parallel-Algorithmus, der ein Minimalgerust fur einen ungerichteten, zusammenhangenden 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 verfugbaren Prozessoren an. Mitn .sup.1-e-Prozessoren lauft er in der ZeitO(n .sup.1+e), wobeie zwischen null und eins liegt. Der Algorithmus ist kostenoptimal, da die Berechnung des Minimalgerusts [OMEGA](n .sup.2) Operationen benotigt. Author Affiliation: (1) Department of Computing and Information Science, Queen's University, Kingston, Ontario, Canada Article History: Registration Date: 18/10/2005 Received Date: 21/01/1985 Article note: This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant NSERC-A3336 (Technical Report No. 85-164).
language: eng
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identifier: ISSN: 0010-485X
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issn:
  • 0010-485X
  • 1436-5057
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descriptionByline: S. G. Akl (1) Keywords: B.3.2 [Memory Structures]: Design Styles -- shared memory; C.1.2 [Computer System Organization]: Multiple Data Stream Architectures (Multi-processors) -- single-instruction-stream, multiple-data-stream processors (SIMD); F.1.2 [Computation by Devices]: Modes of Computation -- parallelism; F.2.2, F.2.3 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems -- computations on discrete structures; Tradeoffs among Complexity Measures; G.2.2 [Discrete Mathematics]: Graph Theory -- graph algorithms, trees; Algorithms; Adaptive algorithm; cost-optimal algorithm; minimum spanning tree; parallel algorithm 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 .sup.1-e processors and runs inO(n .sup.1+e) time wheree lies between 0 and 1 and depends on the number of available processors. In view of the obvious [OMEGA](n .sup.2) lower bound on the number of operations required to compute a minimum spanning tree, the algorithm is also cost-optimal. (German): Wir beschreiben einen Parallel-Algorithmus, der ein Minimalgerust fur einen ungerichteten, zusammenhangenden 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 verfugbaren Prozessoren an. Mitn .sup.1-e-Prozessoren lauft er in der ZeitO(n .sup.1+e), wobeie zwischen null und eins liegt. Der Algorithmus ist kostenoptimal, da die Berechnung des Minimalgerusts [OMEGA](n .sup.2) Operationen benotigt. Author Affiliation: (1) Department of Computing and Information Science, Queen's University, Kingston, Ontario, Canada Article History: Registration Date: 18/10/2005 Received Date: 21/01/1985 Article note: 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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abstractByline: S. G. Akl (1) Keywords: B.3.2 [Memory Structures]: Design Styles -- shared memory; C.1.2 [Computer System Organization]: Multiple Data Stream Architectures (Multi-processors) -- single-instruction-stream, multiple-data-stream processors (SIMD); F.1.2 [Computation by Devices]: Modes of Computation -- parallelism; F.2.2, F.2.3 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems -- computations on discrete structures; Tradeoffs among Complexity Measures; G.2.2 [Discrete Mathematics]: Graph Theory -- graph algorithms, trees; Algorithms; Adaptive algorithm; cost-optimal algorithm; minimum spanning tree; parallel algorithm 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 .sup.1-e processors and runs inO(n .sup.1+e) time wheree lies between 0 and 1 and depends on the number of available processors. In view of the obvious [OMEGA](n .sup.2) lower bound on the number of operations required to compute a minimum spanning tree, the algorithm is also cost-optimal. (German): Wir beschreiben einen Parallel-Algorithmus, der ein Minimalgerust fur einen ungerichteten, zusammenhangenden 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 verfugbaren Prozessoren an. Mitn .sup.1-e-Prozessoren lauft er in der ZeitO(n .sup.1+e), wobeie zwischen null und eins liegt. Der Algorithmus ist kostenoptimal, da die Berechnung des Minimalgerusts [OMEGA](n .sup.2) Operationen benotigt. Author Affiliation: (1) Department of Computing and Information Science, Queen's University, Kingston, Ontario, Canada Article History: Registration Date: 18/10/2005 Received Date: 21/01/1985 Article note: 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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