# Extending Wireless Reschargeable Sensor Network Life without Full Knowledge
## 2 Related Work
### WRSN Scalability  
We focus on WRSN scalability as a network expanding over a large area, as defined in [14]. An optimal solution using linear programming was proposed, after analysing the optimal movement strategies of the MCR [40]. However, solutions requiring high overhead or simply based on sensor node location are impractical for large scale WRSN [41]. Scalability in WRSN has been addressed using several MCR units for charging [39], by defining their coordination and recharging activities. The use of several MCR units led to new questions that needed to be addressed. Identifying the minimum number of MCR units needed to maintain a consistent and efficient charging mechanism was proved to be an NP-Hard problem [42] by reducing it to the Distance Constrained Vehicle Routing Problem. An approximation algorithm was proposed as a solution, where a linear constraint is removed converting the problem to a relaxed version. In another approach [10], an MCR was used to charge another MCR to enable scalability of WRSN charging. While it is possible to show that several nodes can be charged at the same time [9], it only addresses charging high density large-scale WRSN. We provide a solution for large area large-scale WRSN using a single MCR.  
With the increase in WRSN scale, the cost of data propagation significantly increases. In an effort to reduce sensors' energy on reporting data to the sink, studies have been conducted to investigate efficient algorithms to both replenish energy levels of sensors and collect data from them simultaneously [43], or in two stages [44]. Efficient algorithms have been developed to schedule minimum mobile devices for energy replenishment and data collection in a WRSN [45], such that the network life can be prolonged with no limits. Showing this problem is NPC [45]. Combining energy replenishment and data collection with multiple sinks was also shown to be an NP-Hard problem [13], requiring full knowledge of sensors' power levels. A battery-aware mobile energy replenishment and data collection method is proposed in [46] to visit locations such that sensors within the MCR range are charged, while decisions are made according to real-time energy information obtained when visiting head nodes, moving to areas with lower power levels. This approach requires partial knowledge gained while randomly exploring the WRSN. Our work uses a single MCR that only performs charging with no data collection. On the other hand, our work reduces the amount of data propagation, by requiring no power knowledge to be propagated for the charging algorithm.  
As WRSNs scale, the cost of collecting energy information becomes impractical. An efficient energy monitoring protocol was designed to address this problem [39]; however, it assumes the use ofseveral MCR units and each MCR requires full knowledge of the nodes and communication protocols. A high level of integration between the charging system and the actual WRSN operation protocols may become problematic with the scaling of WRSN. Most charging solutions require full knowledge of all sensor nodes' power levels. Full knowledge is also required when addressing the charging problem as an optimization problem [7], where the ratio between the MCR vacation time over cycle time is maximized. While sensor nodes are less energy demanding, most of the energy is consumed by the transceivers [47], and more power can be saved by reducing energy information delegation. This need for energy information in turn limits the scalability of WRSN. We attempt to address WRSN scalability by eliminating the need for a priori energy information.