Algorithm 1 FRER-EDPPS Algorithm

Input: Network topology G, Link failure rate $p_{i,j}$, Node failure rate $p_k$, $(i,j)\in E,k\in V$. Source node s, Destination node d. Output: Working path $P_w$, Redundant path P, Replication node $N_r$, Eliminate node $N_{\mathrm{e}}$.  1: FOR ($i=1$; $i<=N$; i++) 2: FOR ($j=1$; $j<=N$; j++) 3: $R_{i,j}^L\leftarrow (1-p_{i,j})·(1-B_{i,j}^U/B_{i,j}^T)$;//Calculate link status and attribute information 4: $R_k^N\leftarrow (1-p_k)·(1-C_k^U/C_k^T)$;//Calculate node status and attribute information 5: $R^P\leftarrow R_{i,j}^L·R_k^N$;//Calculating path reliability model 6: $W_{i,j}\leftarrow -ln\left(R_{i,j}^P\right)$;//Process path reliability model 7: END FOR 8: END FOR 9: $P_s=\{P_{s1},P_{s2},\dots ,P_{sk}\}\leftarrow Dijkstra(s,G,d)$;//Calculate the shortest path set 10: $P_w\leftarrow P_s\left\{{\left(W_{i,j}\right)}_{max}\right\}$;//Select the path with the highest reliability as the working path 11: $G_1\leftarrow G-E\left(P_w\right)$;//Delete all edges of the working path in G 12: $P_s=\{P_{s1},P_{s2},\dots ,P_{sk}\}\leftarrow Dijkstra(s,G_1,d)$;//Calculate the shortest path set 13: IF $(P_s\ne \varnothing )$//There exist a shortest path 14: $P_r\leftarrow P_s\left\{{\left(W_{i,j}\right)}_{max}\right\}$;//Filter out the path with the highest reliability as a redundant path 15: ELSE 16: $G_2\leftarrow G_1+E\left(P_{w(d\to s)}\right)$;//Add the reverse edge set of the work path to the disconnected graph $G_1$ 17: IF $Dijkstra(s,G_2,d)\to P_s\ne \varnothing$//There are two paths that do not intersect 18: $P_w^{\mathrm{new}},P_r^{new}\leftarrow P_s$; 19: $P_w,P_r\leftarrow P_w^{new},P_r^{new}$;//Calculate two disjoint paths and update them with new working and redundant paths 20: END IF 21: $N_r,N_e\leftarrow Node(P_w\cap P_r)$;//Filter common nodes for working and redundant paths 22: RETURN $P_w,P_r,N_r,N_e$;//Output working path, redundant path, copy nodes, eliminate nodes