Delta-graphs for wireless ad hoc networks

Most topology control algorithms for wireless ad hoc networks strive to reduce energy consumption by creating a sparse topology with few long-distance links. However, in a sparse topology, the average path length is relatively large (increasing end-to-end delay), and the number of vertex-disjoint paths between source-destination pairs is relatively small (reducing fault-tolerance). Unlike traditional topology control algorithms that generate a single topology with a certain property, we propose a distributed algorithm that generates a family of topologies with a range of characteristics. The network designer can choose a suitable topology by simply tuning a single parameter Δ (power savings threshold), trading off energy savings for other features such as low latency and fault-tolerance. For the topologies generated by the proposed algorithm, we also provide an analytical model to estimate their structural density. The accuracy of the analytical model is validated with extensive simulation results.