Timely-efficient and reliable topologies for 3-D sensor networks

Recently, sensor network technology has brought the attention of many researchers due to its scalability and efficiency. However, to improve its efficiency level, several design challenging factors should be taken into account. Among these challenges, we focus on the underlying topology of sensor networks in three-dimensional environments and extend a new set of graphs referred to as the Derived Sphere (DS^α) graphs from their 2-D version [1][30]. We show that DS^α graphs are locally constructed, connected, and have the rotation-ability property. Achieving the connectivity and the rotation-ability properties imply strong reliability for these graphs. Moreover, we show that the new set of graphs has a bounded Euclidean (or length) when 0 < α ≤ 1. Furthermore, via simulations, we confirm and validate these properties. In addition, we demonstrate that DS^α graphs outperform 3-D Half Space Proximal (HSP ) and 3-D Gabriel Graph (GG) graphs in terms of network and Euclidean dilations. This, in turn, increases the speed for message delivery. Therefore, the DS^α graphs are considered timely-efficient graphs.