Distributed Generation of a Family of Connected Dominating Sets in Wireless Sensor Networks

We study the problem of computing a family of connected dominating sets in wireless sensor networks (WSN) in a distributed manner. A WSN is modelled as a unit disk graph G = (V, E) where V and E denote the sensors deployed in the plane and the links among them, respectively. A link between two sensors exists if their Euclidean distance is at most 1. We present a distributed algorithm that computes a family S of S1, S2, · · · , Sm non-trivial connected dominating sets (CDS) with the goal to maximize α = m/k where k=maxu∈V |{i : u ∈ Si}|. In other words, we wish to find as many CDSs as possible while minimizing the number of frequencies of each node in these sets. Since CDSs play an important role for maximizing network lifetime when they are used as backbones for broadcasting messages, maximizing α reduces the possibility of repeatedly using the same subset of nodes as backbones. We provide an upper bound on the value of α via a nice relationship between all minimum vertex-cuts and CDSs in G and present a distributed (localized) algorithm for the α maximization problem. For a subclass of unit disk graphs, we show that our algorithm achieves a constant approximation factor of the optimal solution.