Combined Connectivity Augmentation and Orientation Problems

Two important branches of graph connectivity problems are connectivity augmentation, which consists of augmenting a graph by adding new edges so as to meet a specified target connectivity, and connectivity orientation, where the goal is to find an orientation of an undirected or mixed graph that satisfies some specified edge-connection property. In the present work an attempt is made to link the above two branches, by considering degree-specified and minimum cardinality augmentation of graphs so that the resulting graph admits an orientation satisfying a prescribed edge-connection requirement, such as (k, l)-edge-connectivity. The results are obtained by combining the supermodular polyhedral methods used in connectivity orientation with the splitting off operation, which is a standard tool in solving augmentation problems.