# Joint Deployment of Sensors and Chargers in Wireless
## 2 Related Work  
To deploy static chargers for static sensors, the main research objectives of network deployment are to minimize network deployment cost, maximize charging utility and radiation safety, etc. However, these studies ignore the impact of sensor deployment on the network and only consider the impact of charger deployment on network performance. [PERSON] et al. were the first to consider the connected charger placement problem. In their scenario, given a fixed number of directional wireless chargers and candidate locations, the position and orientation angle of each charger are determined under the connection constraints of wireless chargers to maximize the overall charging utility [27]. [PERSON] et al. considered two inverse problems: minimizing the charger deployment cost constrained by the requirement of charging level and maximizing the charging level constrained by the deployment cost budget of chargers [24]. [PERSON] et al. considered the problem of obstacles and determined the position and direction of heterogeneous chargers with arbitrary shapes on the two-dimensional plane, so as to maximize the charging utility of the network [28]. [PERSON] et al. evaluated the impact of data collection or sink nodes and proposed a two-stage strategy called search most and remove useless [29]. [PERSON] et al. proposed a new cost criterion in multi-hop wireless charging, which is the comprehensive cost composed of energy cost and deployment cost [25]. [PERSON] et al. investigated the impact of obstacles on the placement of wireless chargers to maximize the overall charging utility [30]. [PERSON] et al. proposed an improved Firefly algorithm to solve the charger deployment optimization problem, and furthermore, an optimization framework that simultaneously maximizes the coverage and the charging efficiency [31]. [PERSON] et al. investigated the effect of charger deployment on the overall charging utility of sensor networks. They abstracted the charger deployment problem as a multi-objective optimization problem that maximizes the received power of sensors and minimizes the number of charging sensors [32]. [PERSON] et al. studied the application of WRSNs in indoor environments and used a genetic algorithm to optimize the deployment of chargers in indoor environments [26]. [PERSON] et al. designed a two-stage algorithm to improve the energy management efficiency of WRSNs. The first stage uses a particle swarm optimization algorithm to optimize the area coverage. In the second stage, a queuing game-based energy supply algorithm is designed to optimize the energy  
Figure 1: An illustration of the network model.  
distribution [33]. In these works, little consideration has been given to the impact of sensor deployment on the overall network.  
Table 1 provides a summary of related work for comparison. These efforts provide theoretical basis and insights for our work, but none of them can directly address our problem in three ways. First, we investigate a novel and practical problem for jointly deploying sensors and chargers in static WRSNs with the constraints of deployment cost, which has not been addressed in previous work. Secondly, the impact of sensor deployment on charger deployment is specifically considered. Finally, the new challenge arises from the necessity of proposing approximate solutions with controllable properties such as accuracy and efficiency in the face of the NP-hard of this new problem.