, Volume 18, Issue 1, pp 21–43 | Cite as

An approximation algorithm for minimum-cost vertex-connectivity problems

  • R. Ravi
  • D. P. Williamson


We present an approximation algorithm for solving graph problems in which a low-cost set of edges must be selected that has certain vertex-connectivity properties. In the survivable network design problem, a valuer ij for each pair of verticesi andj is given, and a minimum-cost set of edges such that there arer ij vertex-disjoint paths between verticesi andj must be found. In the case for whichr ij ∈{0, 1, 2} for alli, j, we can find a solution of cost no more than three times the optimal cost in polynomial time. In the case in whichr ij =k for alli, j, we can find a solution of cost no more than 2H(k) times optimal, where\(\mathcal{H}(n) = 1 + \tfrac{1}{2} + \cdot \cdot \cdot + \tfrac{1}{n}\). No approximation algorithms were previously known for these problems. Our algorithms rely on a primal-dual approach which has recently led to approximation algorithms for many edge-connectivity problems.

Key Words

Approximation algorithm Vertex connectivity Survivable network design Primal-dual method 


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Copyright information

© Springer-Verlag New York Inc. 1997

Authors and Affiliations

  • R. Ravi
    • 1
  • D. P. Williamson
    • 2
  1. 1.Graduate School of Industrial AdministrationCarnegie Mellon UniversityPittsburghUSA
  2. 2.IBM TJ Watson Research CenterYorktown HeightsUSA

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