Abstract
In the (k,λ)-subgraph problem, we are given an undirected graph G = (V,E) with edge costs and two parameters k and λ and the goal is to find a minimum cost λ-edge-connected subgraph of G with at least k nodes. This generalizes several classical problems, such as the minimum cost k-Spanning Tree problem or k-MST (which is a (k,1)-subgraph), and minimum cost λ-edge-connected spanning subgraph (which is a (|V(G)|,λ)-subgraph). The only previously known results on this problem [12,5] show that the (k,2)-subgraph problem has an O(log2 n)-approximation (even for 2-node-connectivity) and that the (k,λ)-subgraph problem in general is almost as hard as the densest k-subgraph problem [12]. In this paper we show that if the edge costs are metric (i.e. satisfy triangle inequality), like in the k-MST problem, then there is an O(1)-approximation algorithm for (k,λ)-subgraph problem. This essentially generalizes the k-MST constant factor approximability to higher connectivity.
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Safari, M., Salavatipour, M.R. (2008). A Constant Factor Approximation for Minimum λ-Edge-Connected k-Subgraph with Metric Costs. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2008 2008. Lecture Notes in Computer Science, vol 5171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85363-3_19
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DOI: https://doi.org/10.1007/978-3-540-85363-3_19
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