Probabilistic Analysis of a Parallel Algorithm for Finding Maximal Independent Sets

We consider a natural parallel version of the classical greedy algorithm for finding a maximal independent set in a graph. This version was studied in Coppersmith, Raghavan, and Tompa* and they conjecture there that its expected running time on random graphs of arbitrary edge density of 0 (log n). We prove that conjecture.

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[2]  Prabhakar Raghavan,et al.  Parallel graph algorithms that are efficient on average , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).