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/spl sube/V, with |S|/spl ges/3 and a function g:V/spl rarr/Z/sup +//spl cup/{/spl infin/}, find a smallest set, E', of edges such that (V, E/spl cup/E') has at least two internally-disjoint paths between any pair of vertices in S and such that vertex-degree increase of each /spl nu//spl isin/V by the addition of E' to G is at most g(/spl nu/), where Z/sup +/ is the set of nonnegative integers." The paper shows a linear time algorithm for 2VCA-SV-DC.