Approximate algorithms for sensor deployment with k-coverage in constrained 3D space

Sensor deployment is one fundamental task in sensor network implementation. We generalize and investigate the problem of deploying a minimum set of wireless sensors at candidate locations in constrained 3D space of interest to achieve k-coverage of given target areas such that each point in the target areas is covered by at least k sensors. Based on different constraints on sensor locations and target areas, we formulate four sensor deployment problems: Discrete / Continuous sensor Locations (D/CL) with Discrete / Continuous Target areas (D/CT). We propose an approximate algorithm for DLDT and reduce DLCT and CLDT to DLDT by discretizing continuous sensor locations or target areas into a number of divisions without loss of sensing precision. We further consider the connected version of these four sensor deployment problems where deployed sensors must form a connected network, and propose an approximate algorithm for each of these connected deployment problems.