This paper presents a randomized parallel algorithm for the Maximal Independent Set problem. Our algorithm uses a BSPlike computer with p processors and requires that [Formula: see text] for a graph with n vertices and m edges. Under this scalability assumption, and after a preprocessing phase, it computes a maximal independent set after O( log p) communication rounds, with high probability, each round requiring linear computation time [Formula: see text]. The preprocessing phase is deterministic and important in order to ensure that degree computations can be implemented efficiently. For this, we give an optimal parallel BSPCGM algorithm to the p-quantiles search problem, which runs in [Formula: see text] time and a constant number of communication rounds, and could be of interest in its own right, as shown in the text.
A Simple Parallel Algorithm for the Maximal Independent Set Problem
