## 4 Algorithm Analysis
\begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline
**Algorithm** & \begin{tabular}{c} **Abi-** \\ **ene** \\ \end{tabular} & **Agis** & **Ans** & \begin{tabular}{c} **A19-** \\ **719** \\ \end{tabular} & **A19-** & \
\begin{tabular}{c} **A19-** \\ **723** \\ \end{tabular} & **Att-** & **B20-04** & **Cer-net** &
\begin{tabular}{c} **NJL-** \\ **ATA** \\ \end{tabular} & **USLD** & **V20-08** \\ \hline MCD-BP & 1.10 & 1.08 & 1.06 & 1.07 & 1.20 & 1.06 & 1.09 & 1.05 & 1.26 & 1.12 & 1.21 & 1.27 \\ LFC & 1.05 & 1.07 & 1.13 & 1.05 & 1.09 & 1.01 & 1.38 & 1.14 & 1.02 & 1.28 & 1.12 & 1.03 \\ NPC & 1.05 & 1.06 & 1.05 & 1.05 & 1.09 & 1.01 & 1.07 & 1.02 & 1.02 & 1.11 & 1.06 & 1.03 \\ U-turn & 1.16 & 1.15 & 1.20 & 1.15 & 1.12 & 1.12 & 1.39 & 1.16 & 1.14 & 1.28 & 1.13 & 1.05 \\ MARA & 1.67 & 1.56 & 1.53 & 1.58 & 1.45 & 1.62 & 1.96 & 1.23 & 1.78 & 1.61 & 2.15 & 1.64 \\ \hline \hline
**Algorithm** & **20-4** & **40-4** & **60-4** & **80-4** & **100-4** & **200-2** & **200-4** & **200-6** & **200-8** & **200-10** & **200-12** & \\ \hline MCD-BP & 1.23 & 1.36 & 1.38 & 1.48 & 1.46 & 1.35 & 1.47 & 1.48 & 1.51 & 1.46 & 1.38 & \\ MARA & 3.61 & 3.73 & 4.32 & 4.57 & 4.77 & 2.16 & 2.25 & 2.51 & 3.63 & 3.92 & 4.25 & \\ NPC & 1.41 & 1.39 & 1.02 & 1.49 & 1.46 & 1.24 & 1.46 & 1.52 & 1.63 & 1.63 & 1.64 & \\ U-turn & 1.75 & 1.65 & 1.76 & 1.83 & 1.78 & 1.44 & 1.75 & 1.91 & 1.98 & 1.86 & 1.81 & \\ LFC & 1.75 & 1.68 & 1.75 & 1.82 & 1.77 & 1.33 & 1.74 & 1.89 & 1.96 & 1.87 & 1.83 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Algorithm PSD performance on different topologies. The following table shows the detailed PSD data of different algorithms on various topologies. Figure 11: Comparison of the cross-degree means of the algorithms. The X-axis delineates the names of the actual topologies, while the Y-axis corresponds to cross-degree means. A smaller cross-degree mean indicates superior performance. This figure illustrates this comparison of cross-degree means between the MCD-BP and other algorithms such as LFC, NPC, U-turn, and MARA. These algorithms have been tested on real topologies, namely, Agis, Ans, A19719, A19723, and A19728. As illustrated in Figure 12, the topology AttMpls, B2004, Cernet consistently presents a notably low cross-degree mean across various algorithms. However, the MCD-BP algorithm emerges as the most optimal, registering a cross-degree mean of precisely 0. In the context of topology V2008, several algorithms, namely, LFC, NPC, U-turn, and MARA, exhibit a relatively elevated cross-degree mean. Nevertheless, the MCD-BP algorithm distinctly stands out by displaying the lowest cross-degree mean, markedly differing from the others with a value of 0.16. For perspective, the corresponding cross-degree means for LFC, NPC, U-turn, and MARA are 12.33, 12.33, 12.31, and 15.29, respectively. Upon examination of the experimental results depicted in Figures 13 and 14, it is clear that the MCD-BP algorithm exhibits a significant advantage with respect to minimal cross-degree means, as evidenced by results consistently showing 0 across all simulated topologies. Consequently, in the event of a network fault, this algorithm demonstrates its effectiveness in circumventing it. Figure 13 illustrate that as the topology graph transitions from 20 to 4 to 100-4, the cross-degree mean calculated by the MARA algorithm consistently increases. In contrast, the cross-degree means produced by the other three algorithms remain remarkably similar. For example, in the 80-4 topology, the MCD-BP result is 0, while the values for the LFC, NPC, U-turn, and MARA algorithms are 2.76, 2.75, 2.75, and 4.29, respectively. As illustrated in Figure 14, the MCD-BP algorithm consistently maintains the minimum cross-degree mean, even as the size of the topology increases from 200 to 2 to 200-12. For example, in the 200-2 topology, the MCD-BP algorithm yields a cross-degree mean value of 0, compared to the values of 0, 4.42, 4.42, 4.41, and 6.11 obtained by LFC, NPC, U-turn, and MARA, respectively.