In the survivable network design problem SNDP, the goal is to find a minimum-cost subgraph satisfying certain connectivity requirements. We study the vertex-connectivity variant of SNDP in which the input specifies, for each pair of vertices, a required number of vertex-disjoint paths connecting them. We give the first lower bound on the approximability of SNDP, showing that the problem admits no efficient (formula presented) ratio approximation for any fixed ε > 0 unless NP ⊆ DTIME(npolylog(n)). We also show hardness of approximation results for several important special cases of SNDP, including constant factor hardness for the k-vertex connected spanning subgraph problem (k-VCSS) and for the vertex-connectivity augmentation problem, even when the edge costs are severely restricted.
CITATION STYLE
Kortsarz, G., Krauthgamer, R., & Lee, J. R. (2002). Hardness of approximation for vertex-connectivity network-design problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2462, pp. 185–199). Springer Verlag. https://doi.org/10.1007/3-540-45753-4_17
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