## 4 Algorithm Analysis
\begin{table}
\begin{tabular}{l l l l l l l l l l l l} \hline \hline
**Algorithm** & \begin{tabular}{l} **Abil-** \\ **ene** \\ \end{tabular} & **Ags** & **Ans** & \begin{tabular}{l} **A19-** \\ **719** \\ \end{tabular} & **A19-** & \begin{tabular}{l} **A19-** \\ **723** \\ \end{tabular} & **A19-** & \
\begin{tabular}{l} **Att-** \\ **728** \\ \end{tabular} & **B20-04** & **Cer-net** &
\begin{tabular}{l} **NJL-** \\ **ATA** \\ \end{tabular} & **USD** & **V20-08** \\ \hline MCD-BP & 1.00 & 0.91 & 0.95 & 0.95 & 0.91 & 1.00 & 0.78 & 0.99 & 0.78 & 0.91 & 0.87 & 0.96 \\ LFC & 0.49 & 0.47 & 0.43 & 0.26 & 0.16 & 0.069 & 0.83 & 0.99 & 0.26 & 0.83 & 0.71 & 0.02 \\ NPC & 0.48 & 0.45 & 0.32 & 0.24 & 0.16 & 0.069 & 0.61 & 0.93 & 0.26 & 0.82 & 0.55 & 0.02 \\ U-turn & 0.75 & 0.82 & 0.78 & 0.66 & 0.51 & 0.23 & 0.85 & 0.98 & 0.81 & 0.83 & 0.99 & 0.06 \\ MARA & 0.88 & 0.89 & 0.92 & 0.85 & 0.84 & 0.84 & 0.97 & 0.98 & 0.84 & 0.99 & 0.95 & 0.83 \\ \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 & 0.999 & 0.999 & 0.998 & 0.997 & 0.997 & 0.971 & 0.986 & 0.994 & 1.000 & 1.000 & 1.000 \\ MARA & 0.999 & 0.999 & 0.999 & 0.999 & 1.000 & 0.985 & 0.994 & 0.940 & 0.975 & 0.975 & 0.938 \\ NPC & 0.999 & 0.991 & 0.983 & 0.967 & 0.9749 & 0.745 & 0.948 & 0.983 & 0.997 & 0.998 & 0.985 \\ U-turn & 0.987 & 0.997 & 0.981 & 0.987 & 0.96796 & 0.923 & 0.968 & 0.975 & 0.988 & 0.987 & 0.991 \\ LFC & 0.987 & 0.981 & 0.978 & 0.978 & 0.96599 & 0.763 & 0.958 & 0.975 & 0.986 & 0.986 & 0.993 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Algorithm FPR performance on different topologies. The following table shows the detailed FPR data of different algorithms on various topologies. Figure 6: Experimental results of the failure protection rate. The X-axis delineates the “node count-node degree” simulated topology, while the Y-axis showcases the FPR values. A larger FPR value signifies superior performance. This figure illustrates a comparison of FPR among various algorithms, namely, MCD-BP, LFC, NPC, U-turn, and MARA, when applied to simulated topologies predominantly featuring multi-node polygons. latency. PSD is defined as the ratio of the average backup path length of nodes to the optimal path length [20]. In an ideal scenario, the PSD value is 1. However, in most instances, the backup path length of nodes exceeds the optimal path length. A smaller path stretch indicates less overhead associated with the scheme. We conducted an examination of the PSD of various algorithms in both real and virtual topology. As evidenced by Figure 7, within the real topology, the PSD is lowest under the NPC algorithm, registering a value of 1.01. This is followed by the LFC algorithm at 1.01, the MCD-BP algorithm with a value of 1.06, the U-turn algorithm at 1.12, and finally, the MARA algorithm, which has the highest path stretch index of 1.45. As illustrated in Figure 8, in real topology AttMpls, the NPC algorithm exhibits a distinct advantage in the path stretch metric, recording the minimal path stretch of 1.07 compared to its counterparts. The MCD-BP algorithm follows suit with a path stretch of 1.09, while the U-turn algorithm presents a significantly higher stretch of 1.39. Notably, the experiment reveals that the MARA algorithm yields the highest path stretch, indicating a substantial additional computational overhead introduced to the network by this algorithm. In Figure 9, we note that PSD of the MARA algorithm escalates in direct proportion to the size of the topology graph. Conversely, the performance of the remaining algorithms

Figure 8: Comparison of the path stretching degree of the algorithms. The X-axis delineates the names of the actual topologies, while the Y-axis corresponds to PSD values. The proximity of the PSD value to 1 indicates superior performance.