# Optimizing Charging Pad Deployment by Applying a Quad-Tree Scheme
## 4 Simulation Results
### Performance Comparison of Special Test Maps  
To observe the differences between the results obtained by the proposed method and the optimal ones, we generated several sets of test maps with known optimal solutions using the architecture shown in Figure 10. Initially, we positioned sensors (1-4) in the corners. Due to flying distance constraints, placing sensor 1 requires the use of at least pads 1 and 2 to connect it with the base station. Nevertheless, placing any sensors within the  
Figure 9: Comparisons of (**a**) the required number of pads and (**b**) the average execution time of QT&MSC, QT&MSC&DSC, CDC&MSC methods on extremely large-scale maps. \(D_{maxcharging}\) range of the base station, pad 1, or pad 2 does not require additional pads (the same applies to other corner sensors). In this section, all generated test maps are square network areas of size 8192 \(\times\) 8192, with the base station located at the center. The test maps are divided into four main groups. The first to fourth groups of test maps, respectively, include sensors placed in one to four corners, with the remaining sensors randomly scattered within a specified range according to the number of sensors required. Each group of maps is further subdivided into subcategories ranging from 50, 100, 150, 200,..., to 500 sensors, with 30 maps per subcategory. For example, in the case of the second group with 50 sensors, sensor 1 and sensor 2 are fixed at positions (1, 8192) and (8192, 8192), respectively. The remaining 48 sensors are then randomly distributed within circular areas centered around pad 1, pad 2, pad 3, pad 4, or the base station, with a radius of \(D_{maxcharging}\). Of course, all sensors must be located within the 8192 \(\times\) 8192 network area. Therefore, the total number of test maps in this section is 4 \(\times\) 10 \(\times\) 30. Additionally, the optimal number of pads used in the first to fourth groups of test maps is 3, 5, 7, and 9, respectively. While the optimal number of pads remains constant within the same set of maps regardless of the number of sensors, the results displayed in Figures 11-14 indicate that, in general, the number of pads used increases as the number of sensors in the network increases. This could be attributed to the fact that with more sensors, there are fewer positions that can cover all sensors simultaneously, leading the algorithms to require more  
Figure 10: The basic structure for generating the special test maps. pads to cover all sensors due to deviations in pad placement from the optimal positions. As the complexity of sensor distribution increases from the first group of maps to the fourth group, there is a trend of increasing ratios in the number of pads used by the MSC, GNC, and TNC methods compared to the optimal solution. For maps with 500 sensors, the ratio of pads used by MSC compared to the optimal solution increases from 133.33% to 142.59%, for GNC from 137.78% to 157.04%, and for TNC from 193.33% to 215.19%. In contrast, CDC&DSC remains relatively stable, increasing from 152.22% to 154.81%. However, the method proposed in this paper, QT&MSC, decreases from 124.44% to 114.07%. In terms of computation time, QT&MSC only increases the time by 4.10% to 60.65% compared to MSC, but it is only 0.88% to 1.59% of the time taken by CDC&MSC. The number of pads obtained by QT&MSC is closer to the optimal solution compared to other methods, which may be attributed to its global optimization effect achieved by the QT&MSC method, which subdivides the network as needed from a global perspective. Figure 11: Comparisons of (**a**) the required number of pads and (**b**) the average execution time of related methods on the first group of special test maps. Figure 12: Comparisons of (**a**) the required number of pads and (**b**) the average execution time of related methods on the second group of special test maps.