In this paper, we study distributed approximation algorithms for fault-tolerant clustering in wireless ad hoc and sensor networks. A k-fold dominating set of a graph G = (V,E) is a subset S of V such that every node v \in V \ S has at least k neighbors in S. We study the problem in two network models. In general graphs, for arbitrary parameter t, we propose a distributed algorithm that runs in time O(t^2) and achieves an approximation ratio of O(t\delta^2/t log\delta), where n and \delta denote the number of nodes in the network and the maximal degree, respectively. When the network is modeled as a unit disk graph, we give a probabilistic algorithm that runs in time O(log log n) and achieves an O(1) approximation in expectation. Both algorithms require only small messages of size O(log n) bits.
Citation:
Fabian Kuhn, Thomas Moscibroda, Roger Wattenhofer, "Fault-Tolerant Clustering in Ad Hoc and Sensor Networks," icdcs, pp.68, 26th IEEE International Conference on Distributed Computing Systems (ICDCS'06), 2006