  We present a 6-approximation algorithm for the minimum-cost $k$-node
connected spanning subgraph problem, assuming that the number of nodes is at
least $k^3(k-1)+k$. We apply a combinatorial preprocessing, based on the
Frank-Tardos algorithm for $k$-outconnectivity, to transform any input into an
instance such that the iterative rounding method gives a 2-approximation
guarantee. This is the first constant-factor approximation algorithm even in
the asymptotic setting of the problem, that is, the restriction to instances
where the number of nodes is lower bounded by a function of $k$.
