Given a graph G and target values r(u; v) prescribed for each pair of vertices u and v, we consider the problem of augmenting G by a smallest set F of new edges such that the resulting graph G+F has at least r(u; v) internally disjoint paths between each pair of vertices u and v. We show that the problem is NP-hard even if for some constant k¿ 2 G is (k−1)-vertex-connected and r(u; v)∈{0; k} holds for u; v∈V . We then give a linear time algorithm which delivers a 3 2 -approximation solution to… CONTINUE READING