Combined connectivity augmentation and orientation problems

Abstract

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 has an orientation satisfying a prescribed edge-connection requirement, such as (k, l)-edgeconnectivity. Our proof technique involves a combination of the supermodular polyhedral methods used in connectivity orientation, and the splitting of operation, which is a standard tool in solving augmentation problems.