Hardness of approximation for vertex-connectivity network design problems

Guy Kortsarz, Robert Krauthgamer, James R. Lee

Research output: Contribution to journalArticlepeer-review


In the survivable network design problem (SNDP), the goal is to find a minimum-cost spanning subgraph satisfying certain connectivity requirements. We study the vertex-connectivity variant of SNDP in which the input specifies, for each pair of vertices, a required number of vertex-disjoint paths connecting them. We give the first strong lower bound on the approximability of SNDP, showing that the problem admits no efficient 2 log1-εn ratio approximation for any fixed ε > 0, unless NP ⊆ DTIME(n polylog(n)). We show hardness of approximation results for some important special cases of SNDP, and we exhibit the first lower bound on the approximability of the related classical NP-hard problem of augmenting the connectivity of a graph using edges from a given set.

Original languageEnglish
Pages (from-to)704-720
Number of pages17
JournalSIAM Journal on Computing
Issue number3
StatePublished - 2004
Externally publishedYes


  • Approximation algorithms
  • Connectivity augmentation
  • Hardness of approximation
  • Survivable network design
  • Vertex connectivity


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