Minimizing the Maximum Charging Delay of Multiple Mobile Chargers under the Multi-Node Energy Charging Scheme

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 single sensor can be charged by a mobile charger at each time, this charging scheme however suffers from poor charging scalability and inefficiency. Recently, another charging scheme, the multi-node charging scheme that allows multiple sensors to be charged simultaneously by a mobile charger, becomes dominant, which can mitigate charging scalability and improve charging efficiency. However, most previous studies on this multi-node energy charging scheme focused on the use of a single mobile charger to charge multiple sensors simultaneously. For large scale WRSNs, it is insufficient to deploy only a single mobile charger to charge many lifetime-critical sensors, and consequently sensor expiration durations will increase dramatically. To charge many lifetime-critical sensors in large scale WRSNs as early as possible, it is inevitable to adopt multiple mobile chargers for sensor charging that can not only speed up sensor charging but also reduce expiration times of sensors. This however poses great challenges to fairly schedule the multiple mobile chargers such that the longest charging delay among sensors is minimized. One important constraint is that no sensor can be charged by more than one mobile charger at any time due to the fact that the sensor cannot receive any energy from either of the chargers or the overcharging will damage the recharging battery of the sensor. Thus, finding a closed charge tour for each of the multiple chargers such that the longest charging delay is minimized is crucial. In this paper we address the challenge by formulating a novel longest charging delay minimization problem. We first show that the problem 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 algorithms through experimental simulations. Experimental results demonstrate that the proposed algorithm is promising, and outperforms existing algorithms in various settings.