Abstract

Improving a long chain of works, we obtain a randomised EREW PRAM algorithm for finding the connected components of a graphG=(V, E) withnvertices andmedges inO(logn) time using an optimal number ofO((m+n)/logn) processors. The result returned by the algorithm is always correct. The probability that the algorithm will not complete inO(logn) time iso(n−c) for anyc>0.

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