Optimal Deployment Patterns for Full Coverage and [Formula Omitted]-Connectivity [Formula Omitted] Wireless Sensor Networks

In this paper, we study deployment patterns to achieve full coverage and [Formula Omitted]-connectivity [Formula Omitted] under different ratios of the sensor communication range (denoted by [Formula Omitted]) to the sensing range (denoted by [Formula Omitted]) for homogeneous wireless sensor networks (WSNs). In particular, we propose new patterns for 3- and 5-connectivity. We also discover that there exists a hexagon-based universally elemental pattern that can generate all known optimal patterns. The previously proposed Voronoi-based approach cannot be applied to prove the optimality of the new patterns due to their special features. We propose a new deployment-polygon-based methodology. We prove the optimality of deployment patterns to achieve 3-connectivity, 4-connectivity, and 5-connectivity for certain ranges of [Formula Omitted], respectively, and prove the optimality of deployment patterns to achieve 6-connectivity under all ranges of [Formula Omitted].