Tim Nieberg: Fast Distributed Maximal Independent Set Computation in Bounded Growth Graphs

The distributed complexity of computing a maximal independent set in a graph is of both practical and theoretical importance. While there exists an elegant O(log n) time randomized algorithm for general graphs, no deterministic polylogarithmic algorithm is known. We study the problem in graphs with bounded growth, an important family of graphs which includes the well-known unit disk graph and many variants thereof. Particularly, we present a deterministic algorithm that computes a maximal independent set in time O(log D logstar n) in graphs with bounded growth, where n and D denote the number of nodes and the maximal degree in G, respectively.