A 2-approximation algorithm 2-ABIS for 2-vertex- connectivity augmentation of specified vertices in a graph
The 2-vertex-connectivity augmentation problem for specified vertices (2VCA-SV) is defined as follows: Given an undirected graph G = (V, E), a subgraph G(0) = (V, E') of G, a specified set of vertices S C V and a weight function w : E --> R+ (nonnegative real numbers), find a set E" subset of or equal to E - E' with the minimum total weight, such that G(0) + E" (V, E' boolean OR E") has at least two internally disjoint paths between any pair of vertices in S. In this paper, we propose an O(\Vparallel toE\ + \V\(2) log \V\) time algorithm 2-ABIS, whose performance ratio is 2 (3, respectively), for 2VCA-SV if G(0) has a connected component containing S (otherwise).
graphs augmentation problems performance ratios vertex-connectivity polynomial time algorithms