Enhanced Topological Graphs for 2-D Sensor Networks

For an efficient usage of the sensor technology, several design factors (e.g., topology and sensing coverage) should be taken into account. In this paper, we focus on the underlying topology of sensor networks in two-dimensional environments and enhance a set of recently proposed graphs. The new enhanced graphs are referred to as the Derived Circles version 2 (DC^α v2) graphs. We show that DC^α v2 graphs are locally constructed, connected, have the rotation-ability property, and have the Euclidean Minimum Spanning Tree (EMST) as their subgraphs. Moreover, we show that the new set of graphs has a bounded Euclidean/length and power dilation when 0.5 ≤ α ≤ 1. Furthermore, via simulations, we confirm most of these properties, and demonstrate that the DC^α v2 graphs also have bounded Euclidean and power dilations when 0 <; α <; 0.5. In addition, we demonstrate that DC^α v2 graphs outperform the Half Space Proximal (HSP) and the Relative Neighbourhood Graph (RNG) graphs in terms of the network dilation, Euclidean dilation, and power dilation. This, in turn, increases the speed for message delivery, reduces the energy consumption of nodes and accordingly prolongs the network lifetime.