On virtual-force algorithms for coverage-optimal node deployment in mobile sensor networks via the two-dimensional Yukawa crystal

As theoretical proof has shown that a hexagonal topology can obtain maximal coverage with a fixed number of sensor nodes, node deployment for mobile sensor networks has the objective of forming a hexagonal network topology while consuming minimum energy. Using virtual-force algorithms to move initially randomly distributed nodes into a target topology is one of the widely studied methods for achieving this goal. In this work, a novel virtual-force algorithm based on physical laws in a dusty plasma system (i.e. VFA-DP) was applied within a mobile sensor network deployment scenario. The VFA-DP force has a central attracting force which can provide a screening effect via exponential decay. Here, to evaluate how perfect the final grids become from virtual-force algorithms, we introduce a performance metric based on the pair correlation function in a crystalline structure. Via simulation studies, we determined that the topology resulting from the VFA-DP is much closer to a hexagon. The analysis also indicated that the VFA-DP converges faster than another virtual-force algorithm based on the Lennard-Jones potential (VFA-LJ), resulting in lower communication-related energy costs in real deployment scenarios. The method developed in this article is derived from studies of crystalline structure from condensed matter physics and shows clear evidence of when the regular lattice is ready. It will provide some guidance for engineering by aiding deployment in complex geometric areas or those recovering from disaster.