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 [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 .

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