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The problem of constructing in parallel a maximal independent set of a given graph is considered. A new deterministic NC-algorithm implemented in the EREW PRAM model is presented. On graphs with n vertices and m edges, it uses O((n + m)/log n) processors and runs in O(log³ n) time. This reduces by a factor of log n both the running time and the processor count of the previously fastest deterministic algorithm that solves the problem using a linear number of processors.
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Goldberg et al. (1989) studied this question.
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