Fault-Tolerant Clustering in Ad Hoc and Sensor Networks

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 ∈ 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(t2) and achieves an approximation ratio of O(tΔ2/t logΔ), where n and Δ 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.