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On the PVM computations of transitive closure and algebraic path problems

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Recent Advances in Parallel Virtual Machine and Message Passing Interface (EuroPVM/MPI 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1497))

Abstract

We investigate experimentally, alternative approaches to the distributed parallel computation of a class of problems related to the generic transitive closure problem and the algebraic path problem. Our main result is the comparison of two parallel algorithms for transitive closure,

  • a straightforward coarse-grained parallel implementation of the Warshall algorithm named Block-Processing (which also extends to the stronger algebraic path problem) and

  • a coarse-grained Three-Pass algorithm, introduced in this paper. Although this latter algorithm is more complicated, it behaves better for large problem sizes.

We show the relationship between the transitive closure problem and matrix multiplication — the latter problem has especially efficient PVM implementations which can be applied here. The synchronous shared memory model and several known intricate systolic algorithms are a good starting point for distributed implementations. We discuss alternative implementations and the suitability of the PVM model.

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Authors and Affiliations

  1. Department of Computer Science, University of Liverpool, L69 7ZF, Liverpool, UK

    Ken Chan, Alan Gibbons & Wojciech Rytter

  2. Institute of Informatics, Warsaw University, Warsaw, Poland

    Wojciech Rytter

  3. Department of Computer Science, Fundacao Universidade de Rio Grande, Brazil

    Marcelo Pias

Authors
  1. Ken Chan
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  2. Alan Gibbons
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  3. Marcelo Pias
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  4. Wojciech Rytter
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Editor information

Vassil Alexandrov Jack Dongarra

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© 1998 Springer-Verlag Berlin Heidelberg

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Chan, K., Gibbons, A., Pias, M., Rytter, W. (1998). On the PVM computations of transitive closure and algebraic path problems. In: Alexandrov, V., Dongarra, J. (eds) Recent Advances in Parallel Virtual Machine and Message Passing Interface. EuroPVM/MPI 1998. Lecture Notes in Computer Science, vol 1497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0056593

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  • DOI: https://doi.org/10.1007/BFb0056593

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65041-6

  • Online ISBN: 978-3-540-49705-9

  • eBook Packages: Springer Book Archive

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