Fast connected components algorithms for the EREW PRAM

We present fast and efficient parallel algorithms for finding the connected components of an undirected graph. These algorithms run on the exclusive-read, exclusive-write (EREW) PRAM. On a graph with n vertices and m edges, our randomized algorithm runs in O(logn) time using (m + n1+ǫ)/ logn EREW processors (for any fixed ǫ > 0). A variant uses (m + n)/ logn processors and runs in O(logn log logn) time. A deterministic version of the algorithm runs in O(log n) time using m + n EREW processors.

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