An optimal maximal independent set algorithm for bounded-independence graphs

We present a novel distributed algorithm for the maximal independent set (MIS) problem.1 On bounded-independence graphs (BIG) our deterministic algorithm finishes in O(log n) time, n being the number of nodes. In light of Linial's (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 + 1 coloring and a maximal matching in O(log n) time, where is the maximum degree of the graph. Keywords Ad Hoc Network, Sensor Network, Radio Network, Unit Disk Graph, Growth Bounded Graph, Bounded-Independence Graph, Local Algorithm, Parallel Algorithm, Maximal Independent Set, Maximal Matching, Dominating Set, Connected Dominating Set, Coloring, Symmetry Breaking

• Type: Journal
• Year: 2010
• Where: DC
• Authors: Johannes Schneider, Roger Wattenhofer
• Keywords: Algorithm, DC 2001, DC 2010, Dominating Set, Unit Disk Graph