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

@inproceedings{Dessmark1998UltrafastRP,
  title={Ultrafast Randomized Parallel Construction and Approximation Algorithms for Spanning Forests in Dense Graphs},
  author={Anders Dessmark and Carsten Dorgerloh and Andrzej Lingas and Juergen Wirtgen},
  booktitle={IPPS/SPDP Workshops},
  year={1998}
}
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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