## 4 Algorithm Design
### Fast Rerouting Mechanism  
Fast Reroute (FRR) is a network fault recovery technique. In satellite networks, FRR can be implemented using either backup paths or local repair mechanisms. In the backup path-based FRR mechanism, when the primary path fails, data traffic is switched to the backup path. On the other hand, the local repair-based FRR mechanism involves computing multiple local paths to quickly repair the route near the point of failure. In this paper, we adopt the backup path-based Fast Reroute mechanism (FRR-BP) in the satellite network. In FRR-BP, when a node in the satellite network fails, the network control center removes the failed node from the network topology and recalculates the backup path from the source to the destination. To ensure the stable operation of the satellite network, it is essential to trigger the recalculation of the backup route and swiftly switch to the backup path when a network failure occurs, minimizing the impact of network failures on service quality and reliability. The details of FRR-BP are presented in Algorithm 4. Additionally, it is crucial to be mindful of potential network congestion when employing backup paths. If congestion occurs in the network, the resolution of congestion still necessitates the use of the MOLM algorithm. ```
Input:\(G\), \(Source\), \(Target\), \(path1\), \(length1\), \(path2\), \(length2\), \(fault\_node\) Output:\(path1\), \(path2\)
1 Find the shortest path from \(Source1\) to \(Target1\) by traditional Dijkstra algorithm taking the geographical distance as the weight -> \((path1,length1)\) ;
2 Find the shortest path from \(Source2\) to \(Target2\) by traditional Dijkstra algorithm taking the geographical distance as the weight -> \((path2,length2)\) ;
3 if\(fault\_node\) in \(path2\)then
4 //A node failure occurred, causing the path to be unreachable;
5 Remove \(fault\_node\) in \(path2\) from \(G\) ;
6 Find the shortest path from \(Source2\) to \(Target2\) by traditional Dijkstra algorithm taking the geographical distance as the weight->(\(new\_path,new\_length\));
7 Judge network congestion by calling Algorithm 1 -> \(network\_congestion\) ;
8 if\(network\_congestion\)==0 then
9 \(path2\) = \(new\_path\);
10 \(length2\) = \(new\_length\);
11 print(\(path1,path2\)) ;
12
13 else
14  MOLM(\(T\), \(min\_T\), \(n\), \(max\_n\), \(path1,new\_path\));
15
16
17 else
18 //If there is no disconnection in the path, output the original path  print(\(path1\), \(path2\)) ;
19
20 return\(path1,path2\);
```  
**Algorithm 4**Fast Rerouting method based on backup paths (FRR-BP)  
### Fast Rerouting Mechanism  
Fast Rerouting (FRR) is a network fault recovery technique. In satellite networks, FRR can be implemented using either backup paths or local repair mechanisms. In the backup path-based FRR mechanism, when the primary path fails, data traffic is switched to the backup path. On the other hand, the local repair-based FRR mechanism involves computing multiple local paths to quickly repair the route near the point of failure. In this paper, we adopt the backup path-based Fast Reroute mechanism (FRR-BP) in the satellite network. In FRR-BP, when a node in the satellite network fails, the network control center removes the failed node from the network topology and recalculates the backup path from the source to the destination. To ensure the stable operation of the satellite network, it is essential to trigger the recalculation of the backup route and swiftly switch to the backup path when a network failure occurs, minimizing the impact of network failures on service quality and reliability. The details of FRR-BP are presented in Algorithm 4. Additionally, it is crucial to be mindful of potential network congestion when employing backup paths. If congestion occurs in the network, the resolution of congestion still necessitates the use of the MOLM algorithm.