An Overview of Algorithms for Network Survivability

Algorithm 10

Suurballe-Tarjan-2-link-disjoint-paths (𝐺,𝑠).

(1) Compute the shortest paths tree 𝑇 rooted at 𝑠

(2) Modify the weights of each link (𝑢,𝑣)∈ℒ to 𝑤^′(𝑢,𝑣)=𝑤(𝑢,𝑣)−𝑙(𝑠,𝑣)+𝑙(𝑠,𝑢)

   /*𝑙(𝑠,𝑖) is the length of the shortest path in 𝐺 from 𝑠 to 𝑖^∗/

(3) For 𝑖=1,…,𝑁

(4)    𝑙(𝑖)←∞, 𝑞(𝑖)←𝑁𝐼𝐿, 𝜋(𝑖)←𝑁𝐼𝐿

(5) 𝑙(𝑠)←0

(6) 𝑄←𝒩

(7) While 𝑄≠∅

(8)   EXTRACT-MIN (𝑄)→𝑢

(9)   DELETE (𝑇,𝑢) /*𝑇 becomes a forest of subtrees*/

(10)     For each non-tree link (𝑖,𝑗) in 𝑇 such that 𝑖=𝑢 or 𝑖 and 𝑗 are in different subtrees

(11)      If 𝑙(𝑢)+𝑤(𝑖,𝑗)<𝑙(𝑗)

(12)        𝑙(𝑗)←𝑙(𝑢)+𝑤(𝑖,𝑗),  𝜋(𝑗)←𝑖,𝑞(𝑗)←𝑢