## 4 Results and Discussion  
### Application Case Results of Simplified Nodes  
In this study, clustering analysis is used to assess the importance of each node in the urban gas sensor network, providing a solid foundation for optimizing sensor placement with the ant colony algorithm. Clustering analysis effectively identified the strategic importance of each node, allowing for more precise layout decisions in the subsequent ant colony algorithm optimization process based on these weight factors. Through this  
\begin{table}
\begin{tabular}{c c c} \hline
**Node** & **Scenario** & **Importance** \\ \hline \multirow{2}{*}{1, 2, 8, 13, 17} & Schools, Hospitals, & \multirow{2}{*}{0.8–0.9} \\  & Commercial Areas, etc. & \\ \hline
3, 4, 6, 7, 18 & Parks, etc. & 0.6–0.7 \\ \hline
5, 9, 10, 15, 19 & Roads, Bridges, etc. & 0.4–0.6 \\ \hline
11, 12, 14, 16 & Open Spaces & 0–0.4 \\ \hline \end{tabular}
\end{table}
Table 4: Node weight allocation table.  
\begin{table}
\begin{tabular}{c c} \hline
**Node Spacing** & **Level Coefficient** \\ \hline
50–60 & 0.5 \\ \hline
60–70 & 0.5–0.6 \\ \hline
70–80 & 0.7–0.8 \\ \hline
80–90 & 0.8–0.9 \\ \hline \(>\)90 & 1 \\ \hline \end{tabular}
\end{table}
Table 5: Node distance allocation chart.  
optimization method, the number of sensors is reduced from the initial 19 nodes to 10, while maintaining comprehensive coverage and efficient operation of the monitoring network.  
As shown in Figures 15 and 16, the final optimized sensors were placed at nodes 1, 6, 7, 8, 9, 10, 11, 12, 16, and 17, which played a crucial role in maintaining the integrity of regional monitoring. Each retained node covered key areas, ensuring no blind spots in the monitoring network, significantly improving the system's cost-effectiveness and ease of maintenance. This strategy not only reduced equipment and operational costs but also optimized resource allocation, demonstrating the practical value of data-driven optimization methods in urban infrastructure management.  
Through the optimization process using the ant colony algorithm, we observed changes in sensor coverage with varying numbers of sensors and iterations. For simplicity, the sensor detection range is considered to be 50 m. Figures 3-17 show that, as the number of iterations increases, the coverage rate gradually improves, highlighting the efficiency of the ant colony algorithm in optimizing sensor placement. In configurations with a higher number of sensors, the coverage rate increases quickly and stabilizes rapidly.  
Figure 16: Optimization diagram (after optimization).  
Figure 15: Optimization diagram (before optimization).  
Notably, once the number of sensors reaches a certain level, the coverage rates no longer change significantly, indicating that the system has reached a saturation point where further increases in sensor numbers contribute very little to improving coverage. This phenomenon suggests that moderately increasing the number of sensors effectively enhances coverage, but after reaching the saturation point, excessive sensor deployment leads to resource waste without substantial benefit.  
This finding not only proves the effectiveness of the ant colony algorithm in optimizing sensor placement but also provides valuable theoretical and data support for the design of urban safety monitoring and environmental surveillance systems.