Comprehensive Cost Optimization for Charger Deployment in Multi-hop Wireless Charging

multi-hop wireless charging technology can largely extend the charging service range of chargers, thus has promising prospect in sustainable energy replenishment for wireless rechargeable sensor network. This paper proposes a new cost criterion, termed comprehensive cost consisting of energy cost and deployment cost, to measure the actual expenditure of wireless charging. We present a multi-hop wireless charging model and formulate the problem of minimizing the comprehensive cost such that the energy demand of all sensor nodes can be fulfilled by the energy capacitated chargers. We propose a (ln n + 1)-approximation algorithm for the optimization problem, where n is the number of sensor nodes. Then, we propose a straightforward cost sharing mechanism, which ensures that no subset of sensor nodes can benefit by breaking away from the current charging tree for any fixed charger position, to realize the paid charging service of multi-hop wireless charging. Furthermore, to keep the magnetic fields of transmitters from the interfering, the conflict avoidance schemes are proposed in both central and distributed situations. Finally, we discuss the distributed scheme for minimizing the comprehensive cost without support of central server. Through extensive simulations, we demonstrate the significant superiority of the proposed algorithms in terms of comprehensive cost.