An Optimal Randomised Logarithmic Time Connectivity Algorithm for the EREW PRAM

@article{Halperin1996AnOR,
  title={An Optimal Randomised Logarithmic Time Connectivity Algorithm for the EREW PRAM},
  author={Shay Halperin and Uri Zwick},
  journal={J. Comput. Syst. Sci.},
  year={1996},
  volume={53},
  pages={395-416}
}
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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A simple framework for deterministic graph connectivity in log-diameter steps using label propagation that is easily translated to other computational models and gives the first label propagation algorithms that are competitive with the fastest PRAM algorithms.
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An optimal randomized logarithmic time connectivity algorithm for the EREW PRAM (extended abstract)
TLDR
Improving a long chain of works, a randomized EREW PRAM algorithm is obtained for finding the connected components of a graph G=(V,E) with n vertices and m edges in O(log <italic>n</italic) time using an optimal number of O (+ m + log log) processors.
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