Better algorithms for minimum weight vertex-connectivity problems
Given a k vertex-connected graph with weighted edges, we study the problem of finding a minimum weight spanning subgraph which is k vertex-connected, for small values of k. The problem is known to be NP-hard for any k, even when edges have no weight.
In this paper we provide a 2 approximation algorithm for the cases k=2, 3 and a 3 approximation algorithm for the case k=4. The best approximation factors present in literature are 2, 3 + 2/3 and 4 + 1/6, respectively.
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