Inapproximability of survivable networks

Yuval Lando, Zeev Nutov

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)2122-2125
Number of pages4
JournalTheoretical Computer Science
Issue number21-23
StatePublished - 17 May 2009

Bibliographical note

Funding 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: (Y. Lando), (Z. Nutov).


  • Directed Steiner tree
  • Hardness of approximation
  • Survivable Network Design Problem
  • k-Connected Subgraph


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