Practical Heterogeneous Wireless Charger Placement with Obstacles

Abstract

This paper considers the problem of practical H eterogeneous w I reless charger P lacement with O bstacles (HIPO), i.e., given a number of heterogeneous rechargeable devices distributed on a 2D plane where obstacles of arbitrary shapes exist, deploying heterogeneous chargers with a given cardinality of each type, i.e., determining their positions and orientations, the combination of which we name as strategies , on the plane such that the rechargeable devices achieve maximized charging utility. After presenting our practical directional charging model, we first propose to use a piecewise constant function to approximate the nonlinear charging power, and divide the whole area into multi-feasible geometric areas in which a certain type of chargers have constant approximated charging power. Next, we propose the Practical Dominating Coverage Set extraction algorithm to reduce the unlimited solution space to a limited one by exacting a finite set of candidate strategies for all multi-feasible geometric areas. Finally, we prove the problem falls in the realm of maximizing a monotone submodular function subject to a partition matroid constraint, which allows a greedy algorithm to solve with approximation ratio of $\frac{1}{2} - \epsilon$ 1 2 - e . We conduct experiments to evaluate the performance. Results show that our algorithm outperforms the comparison algorithms by at least 33.49 percent on average.