Journal of Computer Science and Technology

, Volume 8, Issue 4, pp 362–366

# Efficient parallel algorithms for some graph theory problems

• Jun Ma
• Shaohan Ma
Regular Papers

## 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≤pn 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.

## Keywords

Parallel 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)

## References

1. [1]
Floyd, R. W., Algorithm 97: Shortest Path.CACM, 1962, 5(6), p. 345.Google Scholar
2. [2]
Warshall, S., A theorem on Boolean matrices.JACM, 1962, 9(1), pp. 11–12.
3. [3]
Ma Jun and Tadao Takaoka, AnO(n(n 2/p+logp)) parallel algorithm to compute the all pairs shortest paths and the transitive closure.J. of Information Processing of Japan, 1989, 12(2), pp. 119–124.
4. [4]
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
5. [5]
Reghbati, A. E. and Corneil, D. G., Parallel computations in graph theory.SIAM J. Comput., 1978, 2(2), pp. 230–237.
6. [6]
Michael J. Quinn and Naisingh Deo, Parallel graph algorithms.ACM Computing Surveys, 1984, 16 (3), pp. 319–348.
7. [7]
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