# 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 matrix*D* and the path matrix*P* is given. On a PRAM EREW model with*p*,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 array*A* ^{*} of an undirected graph. The time complexity of the parallel algorithm is*O* (*n* ^{3}/*p*). If*D, P* and*A* ^{*} 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 in*O* (*n* ^{2}/*p*+log*p*) 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)## Preview

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## References

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