# Optimizing Charging Pad Deployment by Applying a Quad-Tree Scheme
## 4 Simulation Results
### Performance Comparison
CDC&MSC exhibited a maximum reduction of 7.73% and an average of 7.40%. QT&MSC&DSC decreased by 12.37% at most and 9.59% on average. Therefore, in terms of reducing the number of pads used, QT&MSC is slightly less effective than CDC&DSC, while QT&MSC&DSC performs better than CDC&DSC. However, Figure 7b again highlights the problem of high computational complexity of DSC. Compared with MSC, CDC&DSC increases the calculation time by an average of 4137.68%. QT&MSC and QT&MSC&DSC, respectively, increase the calculation time by an average of 383.26% and 463.92% compared to MSC. When the network scale expands to 8192 \(\times\) 8192, the gap between the proposed methods and MSC widens. As analyzed previously, in environments with 50 to 150 sensors, MSC, GNC, and TNC encounter problems with some maps being unable to find suitable pad configurations. Conversely, our proposed methods and CDC&DSC have no such issues. Excluding scenarios with 50, 100, and 150 sensors, CDC&DSC can reduce the number of pads by up to 10.18%, with an average reduction of 7.21% compared to MSC. Without using DSC, the number of pads used by QT&MSC can be reduced by up to 13.14%, and on average by 10.37%, compared to MSC. The performance of QT&MSC exceeds that of CDC&MSC. Moreover, after combination with DSC, QT&MSC&DSC achieves a maximum reduction of 16.61% and an average reduction of 13.11%. In large-scale network environments, both QT&MSC and QT&MSC&DSC surpass CDC&DSC. The reduction ratio of the average number of pads compared to MSC in CDC&DSC is slightly lower than that in the medium-sized network environment. The average reduction ratio of QT&MSC increases significantly, indicating that QT&MSC is more suitable for large-scale network environments than CDC&DSC. Figure 8b illustrates that CDC&DSC increases the calculation time by 3727.14% on average compared to MSC. QT&MSC and QT&MSC&DSC, respectively, increase the calculation time by 591.29% and 687.13% on average compared to MSC. This is because QT requires more network cutting time for larger network areas and considers more possible locations for placing pads, resulting in better results than MSC, which only considers the locations of sensors. CDC places pads at the center of each cluster after clustering, so the result of clustering determines the quality of the resulting pad configuration. Figure 8 illustrates that in large-size maps, the performance gap between QT&MSC and CDC&DSC tends to widen. Therefore, an additional performance comparison of QT&MSC, CDC&DSC, and QT&MSC&DSC under extremely large maps (16,384 \(\times\) 16,384)  
is included. Since MSC, GNC, and TNC cannot complete pad configuration in this environment, these three methods are excluded from this part of the experiment. In the 8192 \(\times\) 8192 environment, QT&MSC achieves a maximum reduction of 9.84% and an average reduction of 3.39% compared to CDC&DSC, while QT&MSC&DSC achieves a maximum reduction of 10.93% and an average reduction of 6.35%. Figure 9 shows that in a 16,384 \(\times\) 16,384 network environment, the number of pads used by QT&MSC is reduced by up to 9.97% and an average reduction of 9.24% compared to CDC&DSC, while QT&MSC&DSC is reduced by up to 12.05% and an average reduction of 10.82%. On average, the proposed methods tend to perform better than CDC&DSC. Additionally, in terms of usage time, compared to CDC&DSC, the average reduction time of QT&MSC is reduced from 68.70% in Figure 8 to 45.02% in Figure 9, and the average reduction time of QT&MSC&DSC is reduced from 64.12% to 38.18%. This indicates that as the graph size increases, the need for a Quad-Tree to crop the graph also increases, reducing the time advantage of CDC&DSC. In the above experiments, it can be observed that as the sensor density increases, there is a trend of increased pad usage for each method. Additionally, the rate of increase in pad usage tends to slow as sensor density rises.