Using minimum mobile chargers to keep large-scale wireless rechargeable sensor networks running forever

Wireless Rechargeable Sensor Networks (WRSNs) can be recharged after deployment for sustainable operations. Recent works propose to use a single mobile charger (MC) traveling through the network fields to recharge every sensor node. These algorithms work well in small scale networks. However, in large scale networks these algorithms do not work efficiently, especially when the amount of energy the MC can provide is limited. To address these challenges, multiple MCs can be used. In this paper, we investigate the minimum MCs problem (MinMCP) for rechargeable sensor networks: how to find the minimum number of energy-constrained MCs and design their recharging routes given a sensor network such that each sensor node in the WRSN maintains continuous work. Our results are three folds. We first prove that for any ε > 0, there is no (2-ε)-approximation algorithm for Distance Constrained Vehicle Routing Problem (DVRP) on a general metric space, which is the best as far as we know. By reducing from DVRP, we prove that MinMCP is NP-hard, and the inapproximability bound for MinMCP is the same as that of DVRP. Then we propose approximation algorithms for this problem. Finally, we conduct simulations to validate the effectiveness of our algorithms.