## 5 Performance Evaluation
### Efficiency and Computational Complexity Discussion  
In the DHCO algorithm, the most time-consuming procedures were to construct the hierarchical network structure for all sensor nodes and to establish the feasible routing set for each sensor node. For each transmission round, the mean time (in s) and the standard deviation of the computational complexity for the DHCO algorithm were accurately calculated. Table 2 elaborates the statistical results of the computational complexity for the diverse deployment scenarios. We found that the mean time and the standard deviation of the computational complexity were close for all deployment scenarios, except that the mean time rose as the number of sensor nodes increased. Figure 6: Comparison of transmission rounds with different dead sensor nodes for various algorithms in the deployment scenarios of the 100 m \(\times\) 100 m square region and the coordinate (50, 50) of the BS: (**a**) at the 40% dead-sensor-nodes level for different numbers of sensor nodes, and (**b**) at the 80% dead-sensor-nodes level for different numbers of sensor nodes. In consideration of various numbers of sensor nodes, Figure 7 exhibits the comparison of the mean time and standard deviation of the computational complexity for one transmission round in the deployment scenario, in which the region was a 100 m \(\times\) 100 m square and the BS was located at the coordinate (50, 50). In detail, Figure 7a shows that the mean time of the DHCO algorithm for various numbers of sensor nodes was lower than that of state-of-the-art WSN routing algorithms such as LEACH, HEED, GASONeC, and DCFR, and Figure 7b shows that the standard deviation of the computational complexity for the DHCO algorithm was also lower than that of the state-of-the-art WSN routing algorithms. Owing to the fact that the GASONeC algorithm employs more chromosomes in any generation and that more offsprings are created, its computational complexity was the highest. Moreover, according to the hierarchical network structure \(\mathcal{T}\left(\mathcal{V}_{T},\mathcal{E}_{T}\right)\), the DHCO algorithm only needs to choose the optimal route from its established feasible routing set, which contributed to decreasing the scale of the routing optimization problem and the mean computational time. Differently to many conventional WSN routing algorithms (i.e., LEACH, HEED, etc.) that form clusters by using random factors, the DHCO algorithm significantly reduces the effect of randomness, so that the standard deviation of the computational complexity of the DHCO algorithm is the lowest. We found that the DHCO algorithm had a lower computational complexity than the state-of-the-art WSN routing algorithms LEACH, HEED, GASONeC, and DCFR. \begin{table}
\begin{tabular}{c c c c c} \hline
**Width of Square Region** & **Location of BS** & **Number of Nodes** & **Mean Time** & **Standard Deviation** \\ \hline
100 m & (50 m, 50 m) & 100 & 0.00479 s & 0.00011 \\
100 m & (50 m, 50 m) & 120 & 0.00494 s & 0.00014 \\
100 m & (50 m, 50 m) & 140 & 0.00603 s & 0.00018 \\
100 m & (50 m, 50 m) & 160 & 0.00703 s & 0.00016 \\
100 m & (50 m, 50 m) & 180 & 0.00803 s & 0.00012 \\
100 m & (50 m, 50 m) & 200 & 0.00937 s & 0.00013 \\ \hline
100 m & (100 m, 100 m) & 100 & 0.00417 s & 0.00015 \\
100 m & (150 m, 150 m) & 100 & 0.00407 s & 0.00014 \\
100 m & (200 m, 200 m) & 100 & 0.00393 s & 0.00009 \\
100 m & (250 m, 250 m) & 100 & 0.00408 s & 0.00012 \\ \hline
200 m & (50 m, 50 m) & 100 & 0.00409 s & 0.00015 \\
300 m & (50 m, 50 m) & 100 & 0.00389 s & 0.00008 \\
400 m & (50 m, 50m) & 100 & 0.00411 s & 0.00011 \\ \hline \end{tabular}
\end{table} 
Table 2: Statistical Time of Computational Complexity for Various Deployment Scenarios.