We study a heterogeneous two-tier wireless sensor network in which N heterogeneous access points (APs) collect sensing data from densely distributed sensors and then forward the data to M heterogeneous fusion centers (FCs). This heterogeneous node deployment problem is modeled as an optimization problem with the total power consumption of the network as its cost function. The necessary conditions of the optimal AP and FC node deployment are explored in this paper. We provide a variation of Voronoi Diagram as the optimal cell partition for this network and show that each AP should be placed between its connected FC and the geometric center of its cell partition. In addition, we propose a heterogeneous two-tier Lloyd algorithm to optimize the node deployment. Furthermore, we study the sensor deployment when the communication range is limited for sensors and APs. Simulation results show that our proposed algorithms outperform the existing clustering methods like Minimum Energy Routing, Agglomerative Clustering, Divisive Clustering, Particle Swarm Optimization, Relay Node placement in Double-tiered Wireless Sensor Networks, and Improved Relay Node Placement, on average.
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