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We present a novel distributed algorithm for the maximal independent set problem (This is an extended journal version of Schneider and Wattenhofer in Twenty-seventh annual ACM SIGACT-SIGOPS symposium on principles of distributed computing, 2008). On bounded-independence graphs our deterministic algorithm finishes in (log* ) time,  being the number of nodes. In light of Linial’s Ω(log* ) lower bound our algorithm is asymptotically optimal. Furthermore, it solves the connected dominating set problem for unit disk graphs in (log* ) time, exponentially faster than the state-of-the-art algorithm. With a new extension our algorithm also computes a  + 1 coloring and a maximal matching in (log* ) time, where  is the maximum degree of the graph.

An optimal maximal independent set algorithm for bounded-independence graphs