Optimizing Comprehensive Cost of Charger Deployment in Multi-hop Wireless Charging

The multi-hop wireless charging technology has attracted a lot of attention, as it largely extends the charging range of chargers. Different from the existing work with single cost optimization, the objective of this article is to optimize the comprehensive cost, which is the combination of energy cost and deployment cost. We decompose the target problem into two sub-problems. The first sub-problem aims tominimize the deployment cost with energy capacity constraints. The proposed algorithm follows the greedy strategy, where the subset of sensor nodes for any charger is determined by finding the capacitated minimum spanning tree. The second sub-problem, which aims tomaximize the reduction of comprehensive cost by adding chargers to the solution of the first sub-problem, is proved to be an unconstrained submodular set function maximization problem and can be solved by a 1/2-approximation randomized linear time algorithm for its equivalent problem. Through extensive simulations, we demonstrate that the proposed solution can reduce the comprehensive cost by 57.55% comparing with the benchmark algorithms.