a randomized distributed algorithm for the maximal independent set problem in growth-bounded graphs
The efficient distributed construction of a maximal independent set (MIS) of a graph is of fundamental importance. We study the problem in the class of Growth-Bounded Graphs, which includes for example the well-known Unit Disk Graphs. In contrast to the fastest (time-optimal) existing approach [11], we assume that no geometric information (e.g., distances in the graph's embedding) is given. Instead, nodes employ randomization for their decisions. Our algorithm computes a MIS in O (log log n  log* n ) rounds with very high probability for graphs with bounded growth, where n denotes the number of nodes in the graph. In view of Linial's ?(log* n ) lower bound for computing a MIS in ring networks [12], which was extended to randomized algorithms independently by Naor [18] and Linial [13], our solution is close to optimal. In a nutshell, our algorithm shows that for computing a MIS, randomization is a viable alternative to distance information.
randomization distributed algorithms distributed algorithm maximal independent set graph efficiency class examples optimality informal distance embedding computation log probability lower bound network randomized algorithm timing ad hoc sensor networks