Minimum augmentation of local edge-connectivity between vertices and vertex subsets in undirected graphs Original Research Article

Given an undirected multigraph image, a family image of sets image of vertices (areas), and a requirement function image image (where image is the set of nonnegative integers), we consider the problem of augmenting G by the smallest number of new edges so that the resulting graph has at least image edge-disjoint paths between image and W for every pair of a vertex image and an area image. So far this problem was shown to be NP-hard in the uniform case of image for each image, and polynomially solvable in the uniform case of image for each image. In this paper, we show that the problem can be solved in image time, even if image holds for each image, where image, image, image, and image.