Edge-Connectivity Augmentation Problems

The problem in which the object is to add a minimum weight set of edges to a graph so as to satisfy a given condition is called the augmentation problem. This problem has a wide variety [3-5, 10, 11, 14-201. If such a given condition is concerned with the vertexor edge-connectivity of a graph then the problem is referred to as the (vertexor edge-) connectivity augmentation problem. Frank and Chou [S] discussed the unweighted version of some edge-connectivity augmentation problem for graphs without edges, and showed that it is polynomially solvable. Eswaran and Tarjan [3] considered the following problems: (i) The strong connectivity augmentation problem for directed graphs. (ii) The bridge-connectivity augmentation probem for undirected graphs. (iii) The biconnectivity augmentation problem for undirected graphs.