A $(4+epsilon)$-approximation for $k$-connected subgraphs

We obtain approximation ratio $2(2+frac{1}{ell})$ for the (undirected) $k$-Connected Subgraph problem, where $ell approx frac{1}{2} (log_k n-1)$ is the largest integer such that $2^{ell-1} k^{2ell+1} leq n$. For large values of $n$ this improves the $6$-approximation of Cheriyan and Vu0027egh when $n =Omega(k^3)$, which is the case $ell=1...More