Inapproximability of Survivable Networks

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Executive Summary

In the Survivable Network Design Problem (SNDP) one seeks to find a minimum cost subgraph that satisfies prescribed node-connectivity requirements. The authors give a novel approximation ratio preserving reduction from Directed SNDP to Undirected SNDP. Their reduction extends and widely generalizes as well as significantly simplifies the main results. Using it, they derive some new hardness of approximation results, as follows. They show that directed and undirected variants of SNDP and of k-Connected Subgraph are equivalent w.r.t. approximation, and that a p-approximation for Undirected Rooted SNDP implies a p-approximation for Directed Steiner Tree.

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