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 O(log * n) time, n being the number of nodes. In light of Linial's Ω(log * n) lower bound our algorithm is asymptotically optimal. Furthermore, it solves the connected dominating set problem for unit disk graphs in O(log * n) time, exponentially faster than the state-of-the-art algorithm. With a new extension our algorithm also computes a δ + 1 coloring and a maximal matching in O(log * n) time, where δ is the maximum degree of the graph.
Schneider and Wattenhofer present a deterministic algorithm that computes in O(log * n) rounds a connected distance-1 dominating set with constant approximation ratio for bounded-independence graphs REF .
An optimal maximal independent set algorithm for bounded-independence graphs
Distributed Computing
Distributed Computing
Computer Science Engineering