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 Ω(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.
The currently fastest randomized algorithm by Gfeller and Vicari REF runs in O(log log n · log * n) time.
A randomized distributed algorithm for the maximal independent set problem in growth-bounded graphs
PODC '07
Mathematics Computer Science