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 [G. Kortsarz, R. Krauthgamer, J.R. Lee, Hardness of approximation for vertex-connectivity network design problems, SIAM Journal on Computing 33 (3) (2004) 704-720]. 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.
Bibliographical noteFunding Information:
This research was supported by The Open University of Israel’s Research Fund (grant no. 100685). Preliminary version in APPROX, LNCS 5171, pages 146–152. Tel.: +972 9 778 1254; fax: +972 9 778 2605. E-mail addresses: email@example.com (Y. Lando), firstname.lastname@example.org (Z. Nutov).
- Directed Steiner tree
- Hardness of approximation
- Survivable Network Design Problem
- k-Connected Subgraph