Efficient parallel algorithms for some graph theory problems
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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.
KeywordsParallel graph algorithms shortest paths transitive closure connected components diameter of graph center of graph directed cycle with the minimum (maximum) length parallel random access machines (PRAMs)
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- Floyd, R. W., Algorithm 97: Shortest Path.CACM, 1962, 5(6), p. 345.Google Scholar
- Ma Jun and Tadao Takaoka, A parallel algorithm for computing the shortest paths and the transitive closures.Chinese J. of Computers, 13(9) pp. 706–708.Google Scholar
- Hirschberg, D. S., Parallel Algorithms for the transitive closure and the connected component problem. Proc. 8th Annual ACM Symp. on Theory of Computing, ACM, New York, 1976, pp. 55–57.Google Scholar