# Optimizing Charging Pad Deployment by Applying a Quad-Tree Scheme
## 2 Related Works
### Charging Approaches  
Wireless charging vehicles (WCVs) or mobile chargers (MCs) have the capability to wirelessly charge sensor nodes within the network area, which can be 1D, 2D, or 3D. Charger types may include charging vehicles, unmanned aerial vehicles (UAVs), or a combination of both. Previous research on wireless charging for wireless rechargeable sensor networks (WRSNs) has predominantly focused on utilizing WCVs [20; 21; 22; 23; 24] or UAVs [6; 11; 25; 26; 27; 28]. Numerous studies have concentrated on charging sensors using WCVs. For instance, [PERSON] et al. [20] introduced a novel on-demand charging algorithm named the Fuzzy Q-Charging Algorithm, aiming to enhance the network lifespan by optimizing the time and location for MCs to perform charging tasks. Fuzzy Q-charging employs fuzzy logic to determine the optimal charging energy for sensors and proposes a method to identify the optimal charging time for each charging position. This approach utilizes Q-learning to determine the next charging position to maximize the network lifespan. [PERSON] et al. [21] proposed a dual-side charging strategy for mobile charging robot (MR) traversal planning, aimed at minimizing the length, energy consumption, and completion time of the MR's traversal path. Based on MR dual-side charging, adjacent sensors on both sides of the designated path can wirelessly charge via the MR and simultaneously transmit sensory data to the MR. The path construction is based on a power map drawn from the remaining power of sensors in the WRSN and the distance between sensors. Simultaneously, a charging strategy with dual-side charging capability is determined. To minimize network energy consumption, [PERSON] et al. [22] designed an energy-minimization path construction algorithm based on dual-function vehicles for data collection and wireless charging. Their proposed algorithm constructs a mobile vehicle path with anchors for data collection and charging sensor nodes. [PERSON] et al. [23] explored charging sensor nodes with non-deterministic mobility and proposed the Predicting-Scheduling-Tracking approach to execute charging tasks based on the network mechanism. Considering severe node failure problems in networks with high charging demands, [PERSON] et al. [24] addressed the issue by considering the dynamic energy consumption rate of nodes based on historical statistical data and real-time energy consumption. They proposed two efficient online billing algorithms, PA and INMA, where PA selects the next charging node based on the charging probability of the requesting node, and INMA selects the node that minimizes the energy consumption of other requesting nodes as a charging candidate. With the advent of wireless charging UAV technology, several studies have explored the utilization of drones for charging sensors. [PERSON] et al. [6] proposed a method employing a single UAV equipped with pads to charge sensors. They introduced a new model for wireless rechargeable sensor networks (WRSNs) incorporating a UAV and multiple pads strategically deployed to facilitate the UAV's flight path. This model effectively addresses charging challenges by overcoming UAV energy limitations. [PERSON] [11] developed multiple Minimum Depth Trees (MDTs) for all nodes, considering both drone and sensor node energy. The parent node dynamically controls data transmission to prevent its own energy depletion, ensuring balanced data collection for all nodes and preventing energy drain in hotspot areas. In another study, [PERSON] et al. [13] investigated the minimal number of pads required in UAV-based WRSNs. They proposed an adaptive pad deployment scheme capable of accommodating diverse base station locations, geographic distributions of sensor nodes, and network area sizes. [PERSON] et al. [25] tackled the drone scheduling problem to minimize the total charging time for all sensors under energy constraints. They introduced the Drone Scheduling Algorithm (DSA) to optimize UAV scheduling.