Autonomous Deployment for Load Balancing $k$-Surface Coverage in Sensor Networks

Although the problem of $k$-area coverage has been intensively investigated for dense wireless sensor networks (WSNs), how to arrive at a $k$-coverage sensor deployment that optimizes certain objectives in relatively sparse WSNs still faces both theoretical and practical difficulties. Moreover, only a handful of centralized algorithms have been proposed to elevate 2-D area coverage to 3-D surface coverage. In this paper, we present a practical algorithm, i.e., the Autonomous dePlOyment for Load baLancing $k$-surface cOverage (APOLLO), to move sensor nodes toward $k$-surface coverage, aiming at minimizing the maximum sensing range required by the nodes. APOLLO enables purely autonomous node deployment as it only entails localized computations. We prove the termination of the algorithm and the (local) optimality of the output. We also show that our optimization objective is closely related to other frequently considered objectives for 2-D area coverage. Therefore, our practical algorithm design also contributes to the theoretical understanding of the 2-D $k$-area coverage problem. Finally, we use extensive simulation results to both confirm our theoretical claims and demonstrate the efficacy of APOLLO.