# Efficient Wireless Charger Deployment for Wireless Reshapeable Sensor Networks
## 2 Related Work
The upper and lower bounds of QoEP in 1D and 2D sensor node mobility cases are derived. [PERSON] et al. [7] considered the scheduling problem of arranging multiple mobile chargers to collaboratively charge sensor nodes with the goal of minimizing the total traveling distance of all chargers. This can be formulated as finding multiple travelling salesperson problem (TSP) closed tours covering all sensor nodes such that the total length of the tours is minimized. The authors proposed a 2-approximation algorithm to solve the problem under the assumption that the energy consumption rates of all sensor nodes are fixed. [PERSON] et al. [8] considered a scheduling problem similar to that addresses by [PERSON] et al. in [6]. The problem is how to use the minimum number of mobile chargers to charge sensor nodes so that none of sensor nodes runs out of energy, subject to the energy capacity of mobile chargers. The authors designed a 5-approximation algorithm to find multiple closed tours. Afterwards, by bounding the total distance of each tour, the authors designed another approximation algorithm invoking the 5-approximation algorithm to provide approximate solutions to the problem. [PERSON] et al. [9] introduced a new metric, the charging utility, to measure the charging quality of the charger with the considerations of both the fairness of charging sensor nodes and the number of sensor nodes charged by mobile chargers traveling along closed tours. It is assumed that each mobile charger can only travel a limited length per tour, due to its limited energy capacity. The authors formulated an optimization problem of scheduling a mobile charger to charge sensor nodes, with an objective of maximizing the charging utility, subject to the total traveling distance of the mobile charger per tour and the deadline of each sensor node to be charged. An approximation algorithm with a guaranteed approximation ratio was proposed to solve the problem. [PERSON] et al. [14] proposed a WPT scheme called multi-point carrier shift diversity (MPCSD), in which the center frequency of the carrier of each power transmitting point (or transmitter) is slightly shifted with a predefined amount to create artificial fading. Suppose there are \(N\) different transmitters, the carrier frequency \(f_{n}\) of the \(n\)th transmitter is defined in Equation (3), shown below:  
\[f_{n}=f_{\mathrm{c}}-\ \frac{B}{2}+\frac{(2n-1)\ B}{2N} \tag{3}\]  
In Equation (3), \(f_{\mathrm{c}}\) is the center frequency, \(B\) is the channel bandwidth, and \(n=1,\ldots,N\). The proposed scheme is shown to be capable of mitigating power attenuation caused by the path loss effect and the standing-wave effect created by multipath and interference between multiple power transmitters so that the coverage of energy supply field is improved. [PERSON] et al. [15] investigated the energy transmission coverage of the MPCSD scheme through theoretical discussions and practical experiments. It is shown that the MPCSD scheme can achieve 100% of coverage in an indoor environment for the sensor node duty factor of 1/100 (i.e., the sensor node is in the transmitting mode for the duration of 10 ms per second). [PERSON] et al. [16] conducted experiments in an IEEE 802.11g-based wireless local area network (WLAN) in which an ES transmits microwave power to a sensor station (SS) using the carrier sense multiple access with collision avoidance (CSMA/CA) protocol to transmit data to an access point (AP). They derived the following two requirements for coexistence of MPT and the WLAN wireless data transmission (WDT). First, MPT and WDT should not proceed simultaneously. Therefore, the ES should share the timing information of MPT with the SS so that the SS attempts to transmit data frames only when the ES does not transmit microwave power. Second, the ES should not transmit microwave power to the SS when the AP broadcasts beacon frames so that the SS is not disassociated from the AP. This can also prevent data throughput degradation due to WLAN automatic data rate selection. [PERSON] et al.