Distributed topology control in wireless ad hoc networks using β-skeletons

We propose a novel approach for sparse topology generation in wireless ad hoc networks based on a graph structure known as beta-skeletons. Two efficient algorithms are presented in this paper for creating a connected topology from an underlying beta-skeleton. One algorithm is a distributed algorithm that runs on each component of the beta-skeleton. It creates a connected structure from the disconnected beta-skeleton graph using a distributed leader election algorithm. The running time of this algorithm is 0 (n log n). The other is a localized algorithm that uses two-hop neighborhood information to generate a connected topology, with a running time of 0(n). Simulations show consistent decrease in node degree in the resulting topology. The observed decrease is greater than 33% in comparison to the Relative Neighborhod Graph (RNG) and greater than 50% in comparison to other topology structures such as, the Gabriel Graph (GG) and the Yao construction on GG.