Ultrafast Randomized Parallel Construction and Approximation Algorithms for Spanning Forests in Dense Graphs

We present a first randomized $\O$$(\log^{(k)} n)$ time and $\O$$(n + m)$ work CRCW-PRAM algorithm for finding a spanning forest of an undirected dense graph with $n$ vertices. Furthermore we construct a randomized $\O$$(\log \log n)$ time and $\O$$(n \log n)$ work CREW-PRAM algorithm for finding spanning trees in random graphs. Our algorithm is optimal with respect to time, work and space.

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