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In the survivable networkdesign problem (SNDP), the goal is to find a minimum-cost spanning subgraph satisfying certain connectivity requirements. We study the vertex-connectivity variant of SNDP in which the input specifies, for each pair of vertices, a required number of vertex-disjoint paths connecting them. We give the first strong lower bound on the approximability of SNDP, showing that the problem admits no efficient 2^^{1- n} ratio approximation for any fixed \! >\! 0, unless (n^ (n) ). We show hardness of approximation results for some important special cases of SNDP, and we exhibit the first lower bound on the approximability of the related classical NP-hard problem of augmenting the connectivity of a graph using edges from a given set.
Kortsarz et al. (Thu,) studied this question.