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Efficient parallel algorithms for some graph theory problems

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Abstract

In this paper, a sequential algorithm computing the all vertex pair distance matrixD and the path matrixP is given. On a PRAM EREW model withp,1≤p≤n 2, processors, a parallel version of the sequential algorithm is shown. This method can also be used to get a parallel algorithm to compute transitive closure arrayA * of an undirected graph. The time complexity of the parallel algorithm isO (n 3/p). IfD, P andA * are known, it is shown that the problems to find all connected components, to compute the diameter of an undirected graph, to determine the center of a directed graph and to search for a directed cycle with the minimum (maximum) length in a directed graph can all be solved inO (n 2/p+logp) time.

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Authors and Affiliations

  1. Dept. of Computer Science, Shandong University, 250100, Jinan

    Jun Ma & Shaohan Ma

Authors
  1. Jun Ma
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  2. Shaohan Ma
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Research supported by the Science Foundation of Shandong Province.

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Ma, J., Ma, S. Efficient parallel algorithms for some graph theory problems. J. of Compt. Sci. & Technol. 8, 362–366 (1993). https://doi.org/10.1007/BF02939544

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  • DOI: https://doi.org/10.1007/BF02939544

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