Abstract
In the Survivable Network Design Problem (SNDP) one seeks to find a minimum cost subgraph that satisfies prescribed node-connectivity requirements. We give a novel approximation ratio preserving reduction from Directed SNDP to Undirected SNDP. Our reduction extends and widely generalizes as well as significantly simplifies the main results of [6]. Using it, we derive some new hardness of approximation results, as follows. We show that directed and undirected variants of SNDP and of k -Connected Subgraph are equivalent w.r.t. approximation, and that a ρ-approximation for Undirected Rooted SNDP implies a ρ-approximation for Directed Steiner Tree.
This research was supported by The Open University of Israel’s Research Fund (grant no. 100685).
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Lando, Y., Nutov, Z. (2008). Inapproximability of Survivable Networks. 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_12
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DOI: https://doi.org/10.1007/978-3-540-85363-3_12
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