A (4+ε)-approximation for k-connected subgraphs
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We obtain approximation ratio 2(2+1/ℓ) for the (undirected) k-Connected Subgraph problem, where ℓ≈1/2 (_k n-1) is the largest integer such that 2^ℓ-1 k^2ℓ+1≤ n. For large values of n this improves the 6-approximation of Cheriyan and Végh when n =Ω(k^3), which is the case ℓ=1. For k bounded by a constant we obtain ratio 4+ϵ. For large values of n our ratio matches the best known ratio 4 for the augmentation version of the problem, as well as the best known ratios for k=6,7. Similar results are shown for the problem of covering an arbitrary crossing supermodular biset function.
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