A 4 + ε approximation for k-connected subgraphs

We obtain approximation ratio (equation presented) for the (undirected) k-Connected Subgraph problem, where l = (equation presented) is the largest integer such that 2^l−1k^2l+1 ≤ n. For large values of n this improves the ratio 6 of Cheriyan and Végh [4] when n ≥ k³ (the case l = 1). Our result implies an fpt-approximation ratio 4 + ε that matches (up to the “+ε” term) the best known ratio 4 for k = 6, 7 for both the general and the easier augmentation versions of the problem. Similar results are shown for the problem of covering an arbitrary crossing supermodular biset function.