## 4 Algorithm Analysis
The subsequent Table 5 presents the specific experimental data pertaining to FPR. Figure 12: 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, AttMpls, B2004, Cernet, NJLATA, USLD, V2008. Figure 14: Comparison of the cross-degree means of the algorithms. The X-axis delineates the “node count-node degree” simulated topology, while the Y-axis showcases the cross-degree means values. A smaller cross-degree mean indicates superior performance. This figure depicts a comparative analysis of cross-degree means of the multi-node polygon simulation topologies, contrasting the MCD-BP algorithm against the LFC, NPC, U-turn, and MARA algorithms. Figure 13: Comparison of the cross-degree means of the algorithms. The X-axis delineates the “node count-node degree” simulated topology, while the Y-axis showcases the cross-degree means. A smaller cross-degree mean indicates superior performance. This figure depicts a comparative analysis of cross-degree means on simulated topologies with a small number of nodes, contrasting the MCD-BP algorithm against the LFC, NPC, U-turn, and MARA algorithms. \begin{table}
\begin{tabular}{l l l l l l l l l l l l} \hline \hline
**Algorithm** & **Agis** & **Ans** & **A19-719** & **A19-723** & **A19-728** & **Att-Mpls** & **B20-04** & **Cer-net** & **NJL-ATA** & **USLD** & **V20-08** \\ \hline MCD-BP & 0 & 0 & 0.08 & 0.23 & 0.08 & 0 & 0 & 0.13 & 0 & 0 & 0.16 \\ LFC & 2.40 & 2.51 & 3.09 & 4.21 & 4.51 & 2.21 & 1.82 & 2.53 & 1.73 & 3.16 & 12.33 \\ NPC & 2.41 & 2.52 & 3.11 & 4.19 & 4.50 & 2.23 & 1.84 & 2.55 & 1.75 & 3.18 & 12.33 \\ U-turn & 2.34 & 2.43 & 2.98 & 4.03 & 4.49 & 2.20 & 1.81 & 2.52 & 1.73 & 3.13 & 12.31 \\ MARA & 3.39 & 3.37 & 3.51 & 4.76 & 5.51 & 3.98 & 1.98 & 3.63 & 2.01 & 4.95 & 15.29 \\ \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 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ MARA & 2.42 & 3.22 & 3.93 & 4.29 & 4.73 & 6.11 & 6.32 & 6.51 & 6.87 & 7.34 & 7.98 \\ NPC & 1.56 & 2.16 & 2.49 & 2.75 & 3.01 & 4.42 & 3.62 & 3.11 & 2.98 & 2.76 & 2.67 \\ U-turn & 1.56 & 2.15 & 2.50 & 2.75 & 2.98 & 4.41 & 3.61 & 3.12 & 2.99 & 2.75 & 2.64 \\ LFC & 1.57 & 2.17 & 2.48 & 2.76 & 3.01 & 4.42 & 3.62 & 3.09 & 2.99 & 2.73 & 2.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Algorithm cross-degree means performance on different topologies. The following table shows the detailed cross-degree mean data of different algorithms on various topologies. ### Robustness

Considering that the network topology and parameter configuration remain unaltered in this experiment, and given the fully deterministic nature of the algorithm execution process, the experimental environment effectively eliminates the impact of random factors. Therefore, it can be concluded that under these fixed experimental conditions, the performance outcomes exhibited by this algorithm are reflective of the system's inherent attributes, thus demonstrating its robustness. ## 7 Discussion

The experimental results detailed in Section 4 demonstrate that the MCD-BP algorithm offers substantial benefits in terms of the FPR. Notably, it consistently achieves superior FPR across various real and simulated topologies, including notable real topologies like Abilene and A19728, as well as simulated topologies such as 200-8, 200-10, and 200-12. In these scenarios, FPR attains a value of 1, signifying that the algorithm is adept at providing reliable backup paths for data transmission, thereby significantly mitigating the consequences of network failure.