Efficient parallel algorithms for some graph theory problems
Efficient Parallel Algorithms for Some Graph Theory Problems

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. Research supported by the Science Foundation of Shandong Province.