Degree constrained topology control for very dense wireless sensor networks

We present a novel topology control algorithm for very dense wireless sensor networks that is constrained by a small maximum nodal degree k. Particularly, we limit k=4 which makes it challenging to formulate a connected network that possesses favorable properties such as a small diameter, short average path length and low energy consumption. Towards this goal, we introduce a graph theoretic approach that utilizes a Borel Cayley Graph as an underlying network topology. We call this approach Borel Cayley Graph Topology Control (BCG-TC). Simulation results for a network with 1081 nodes distributed over a 100mx100m area showed that BCG-TC can formulate connected networks for the radio range exceeding certain threshold. Furthermore, these connected networks generated by BCG-TC exhibit (i) a small nodal degree k≤4, (ii) a small diameter and short average path length, and (iii) fast information dissemination that leads to the least energy consumption among considered topology control protocols.