Fast deterministic distributed maximal independent set computation on growth-bounded graphs

Abstract

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 [20], no deterministic polylogarithmic algorithm is known. In this paper, 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 propose a deterministic algorithm that computes a maximal independent set in time O(log Δ · log*n) in graphs with bounded growth, where n and Δ denote the number of nodes and the maximal degree in G, respectively. © Springer-Verlag Berlin Heidelberg 2005.