A Randomized Time-Work Optimal Parallel Algorithm for Finding a Minimum Spanning Forest

We present a randomized algorithm to find a minimum spanning forest (MSF) in an undirected graph. With high probability, the algorithm runs in logarithmic time and linear work on an EREW PRAM. This result is optimal with respect to both work and parallel time, and is the first provably optimal parallel algorithm for this problem under both measures.

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