A 2-approximation algorithm to (k+1)-edge-connect a specified set of vertices in a k-edge-connected graph
The (k + delta)-edge-connectivity augmentation problem for a specified set of vertices ((k + delta)ECA-SV) is defined as follows: "Given an undirected graph G = (V, E), a specified set of vertices Gamma subset of V, a subgraph G' = (V, E') with lambda(F; G') = k of G and a cost function c: E -> Z(+) (nonnegative integers), find a set E* subset of E - E' of edges, each connecting distinct vertices of V, of minimum total cost such that lambda(Gamma; G") >= k + delta for G" = (V, E' boolean OR E*)," where lambda(Gamma; G") is the minimum value of the maximum number of edge disjoint paths between any pair of vertices in Gamma of G". The paper proposes an O(Delta + vertical bar V vertical bar vertical bar E vertical bar) time 2-approximation algorithm FSAR for (k + 1)ECA-SV with a restriction lambda(V; G') = lambda(Gamma; G'), where Delta is the time complexity of constructing a structural graph of a given graph G'.
graphs augmentation problems edge-connectivity approximation algorithms