Minimum augmentation to bi-connect specified vertices of a graph with upper bounds on vertex-degree

The 2-vertex-connectivity augmentation problem for a specified set of vertices of a graph with degree constraints (2VCA-SV-DC) is defined as follows. "Given an undirected graph, G=(V, E), a specified set of vertices, S⊆V, with |S|≥3 and a function g:V→Z⁺∪{∞}, find a smallest set, E\´, of edges such that (V, E∪E\´) has at least two internally-disjoint paths between any pair of vertices in S and such that vertex-degree increase of each ν∈V by the addition of E\´ to G is at most g(ν), where Z⁺ is the set of nonnegative integers." The paper shows a linear time algorithm for 2VCA-SV-DC.