# Joint Deployment of Sensors and Chargers in Wireless
## 1 Introduction  
Traditional wireless sensor networks (WSNs) are distributed networks composed of a large number of sensors that can perceive the external world. Sensors usually have the characteristics of small size, convenient deployment, low cost, and easy networking. Normally, battery-powered sensors with limited capacity tend to be out of service after frequenting wireless communication and data perception, which limits the continuous work of the WSNs. Also, sensors are sometimes located in dangerous or hard-to-reach areas, such as near volcanoes [1], inside concrete walls [2], or under bridges [3], making battery replacement schemes unsafe [4; 5; 6], as well as infeasible or costly. In order to solve this problem, much literature has proposed methods of energy saving [7; 8] and energy acquisition [9]. Energy saving methods can extend the service life but cannot inherently solve the energy problem of WSNs. The energy harvesting method allows sensors to harvest energy from the surrounding environment, but many energy sources, such as thermal energy [10], wind energy [11; 12], etc., are unpredictable and unreliable. The recent breakthrough in radio-frequency radiation charge technology brings new opportunities to solve this problem [13]. A major feature of wireless rechargeable sensor networks (WRSNs) is that their lifetime is no longer restricted by batteries, and wireless chargers can continuously and stably provide energy supply for sensor networks; thus, they have been used in smart grids [14], body sensor networks [15] and civil structure monitoring [16]. Among the research aspects of WRSNs, the deployment strategies of key devices, such as sensors and chargers, play important roles in the optimization of deployment cost, network performance, etc., and thus have been a hot topic. In the existing efforts, three typical scenarios are usually involved: (1) deploying static chargers to charge static sensors; (2) deploying mobile chargers to charge static sensors; and (3) deploying static chargers to charge mobile sensors. The first scenario is the most common and usually studies network utility maximization, delay minimization, and routing protocols [17; 18; 19]. The second scenario can be roughly divided into single mobile charger (MC) charging schemes and multi-MC charging schemes, which are constrained by network lifetime, path planning, coverage, monitoring efficiency, and so on [20; 21]. The third scenario is common in monitoring mobile WSNs, such as in applications like industrial wireless identification and healthcare [22; 23]. In the first scenario, previous efforts have been mainly focused on the deployment problem of static chargers. To optimize the deployment cost of chargers, the optimal charging coverage of the charger for sensors is studied in [24; 25; 26]. To maximize the charging utility, the optimal deployment strategy for chargers is studied in [27; 28; 29; 30; 31; 32]. However, these works tend to overlook the deployment of sensors or directly utilize the distribution of sensors generated pseudo-randomly, thereby ignoring the impact of sensor deployment on subsequent charger deployment. This has been proven to be undeniable in our subsequent research. Therefore, we study a new problem, namely the joint deployment problem of chargers and sensors, and specifically, the sensors are deployed to monitor the points of interest (Pols). As shown in Figure 1, Pols are randomly and densely distributed in a two-dimensional plane. The deployed sensors have an aggregation effect, which is presented by deploying new sensors that are close to the deployed sensors. For example, in Figure 1, the sensors at candidate locations 1 and 2 have similar sensing reliability, but candidate location 1 is closer to the deployed sensors than candidate location 2, and thus, the next sensor is deployed at candidate location 1.