Hardness of Approximation for Vertex-Connectivity Network-Design Problems

  • Guy Kortsarz
  • Robert Krauthgamer
  • James R. Lee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2462)

Abstract

In the survivable network design problem SNDP, the goal is to find a minimum-cost 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 vertexdisjoint paths connecting them.

We give the first lower bound on the approximability of SNDP, showing that the problem admits no efficient \( 2^{\log ^{1 - \in } n} \) ratio approximation for any fixed ∈>0 unless NP ⊆ DTIME(npolylog(n)). We also show hardness of approximation results for several important special cases of SNDP, including constant factor hardness for the k-vertex connected spanning subgraph problem (k-VCSS) and for the vertex-connectivity augmentation problem, even when the edge costs are severely restricted.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Guy Kortsarz
    • 1
  • Robert Krauthgamer
    • 2
  • James R. Lee
    • 3
  1. 1.Department of Computer SciencesRutgers UniversityCamdenUSA
  2. 2.International Computer Science Institute (ICSI) and Computer Science DivisionUniversity of CaliforniaBerkeleyUSA
  3. 3.Computer Science DivisionUniversity of CaliforniaBerkeleyUSA

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