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In the k-2VC problem, we are given an undirected graph G with edge costs andan integer k; the goal is to find a minimum-cost 2-vertex-connected subgraph ofG containing at least k vertices. A slightly more general version is obtainedif the input also specifies a subset S \subseteq V of terminals and the goal isto find a subgraph containing at least k terminals. Closely related to thek-2VC problem, and in fact a special case of it, is the k-2EC problem, in whichthe goal is to find a minimum-cost 2-edge-connected subgraph containing kvertices. The k-2EC problem was introduced by Lau et al., who also gave apoly-logarithmic approximation for it. No previous approximation algorithm wasknown for the more general k-2VC problem. We describe an O(\log n \log k)approximation for the k-2VC problem.

Min-Cost 2-Connected Subgraphs With k Terminals