A 2-approximation algorithm FSA+1 to (λ+1)-edge-connect a specified set of vertices in a λ-edge-connected graph

The k-edge-connectivity augmentation problem for a specified set of vertices (kECA-SV) is defined as follows: "Given an undirected graph G=(V, E), a subgraph G\´=(V, E\´) of G, a specified set of verticies Γ⊆V and a cost function c: E→Z⁺ (non-negative integers), find a set E"⊆E-E\´ of edges, each connecting distinct vertices of V, of minimum total cost such that λ(Γ; G\´+E")≥k for G\´+E"=(V, E\´∪E")," where λ(Γ; G")≥k means that G" has at least k edge disjoint paths between any pair of vertices in Γ. The paper proposes an O(Δ+|V||E|) time 2-approximate algorithm FSA+1 for (λ+1)ECA-SV with λ(V; G)=λ(Γ; G), where λ=λ(Γ; G\´) and Δ is the time complexity of constructing a structural graph of a given graph G\´.