Using Local Geometry for Tunable Topology Control in Sensor Networks

Neighbor-Every-Theta (NET) graphs are such that each node has at least one neighbor in every theta angle sector of its communication range. We show that for theta < pi, NET graphs are guaranteed to have an edge connectivity of at least left perpendicular 2 pi/theta right perpendicular, even with an irregular communication range. Our main contribution is to show how this family of graphs can achieve tunable topology control based on a single parameter theta. Since the required condition is purely local and geometric, it allows for distributed angle-only topology control. For a static network scenario, a power control algorithm based on the NET condition is developed for obtaining k-connected topologies and shown to be significantly efficient compared to existing schemes. In the controlled deployment of a mobile network, control over positions of nodes can be leveraged for constructing NET graphs with desired levels of network connectivity and sensing coverage. To establish this, we develop a potential fields-based distributed controller and present simulation results for a large network of robots. Last, we extend NET graphs to 3D and provide an efficient algorithm to check for the NET condition at each node. This algorithm can be used for implementing generic topology control algorithms in 3D.