Minimizing the longest charge delay of multiple mobile chargers for wireless rechargeable sensor networks by charging multiple sensors simultaneously

Wireless energy charging has emerged as a very promising technology for prolonging sensor lifetime in Wireless Rechargeable Sensor Networks (WRSNs). Existing studies focused mainly on the 'one-to-one' charging scheme that a sensor can be charged by a single mobile charger at each time, this charging scheme however suffers from poor charging scalability and inefficiency. Recently, another charging scheme - the 'multiple-to-one' charging scheme that allows multiple sensors to be charged simultaneously by a single charger, becomes dominant and can mitigate charging scalability and improve the charging efficiency. Most research studies on this latter scheme focused on the use of a mobile charger to charge multiple sensors simultaneously. However, for large scale WRSNs, it is insufficient to deploy just a single mobile charger to charge many lifetime-critical sensors, and consequently sensor expiration durations will increase dramatically. Instead, in order to charge as many as lifetime-critical sensors, the use of multiple mobile chargers for charging sensors can speed up sensor charging significantly, thereby reducing their expiration durations and improving the monitoring quality of WRSNs. However, this poses great challenges to schedule multiple mobile chargers for sensor charging at the same time such that the longest delay among the chargers is minimized due to multiple critical constraints. One such an important constraint in multiple mobile chargers is that each sensor cannot be charged by more than one mobile charger at each time; otherwise, the sensor cannot receive any energy from either of the chargers. In this paper we address this challenge by first formulating a novel longest delay minimization problem that is NP-hard. We then devise the very first approximation algorithm with a provable approximation ratio for the problem. We finally evaluate the performance of the proposed algorithm through experimental simulations. Simulation results demonstrate that the proposed algorithm is very promising, which outperforms the other heuristics in various settings.