Augmenting edge and vertex connectivities simultaneously

Abstract

Given an undirected multigraph G = (V, E) and requirement functions (Formula Presented) and (Formula Presented) (where Z + is the set of nonnegative integers), we consider the problem of augmenting G by the smallest number of new edges so that the edge-connectivity and vertexconnectivity between every pair x,y Є V become at least rλ (x,y) and rk(x,y), respectively, in the resulting graph Gʹ. In this paper, we show that the problem can be solved in polynomial time if rλ is given by rk(x,y) = 2 for all x,y Є V.