Inapproximability of Survivable Networks

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 [9]. 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 -approximation for Undirected Rooted SNDP implies a -approximation for Directed Steiner Tree.

• Type: Conference
• Year: 2008
• Where: APPROX
• Authors: Yuval Lando, Zeev Nutov
• Keywords: Algorithms, APPROX 2008, Minimum Cost Subgraph, Undirected, Undirected SNDP