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Combinatorica

, Volume 15, Issue 3, pp 435–454 | Cite as

A primal-dual approximation algorithm for generalized steiner network problems

  • David P. Williamson
  • Michel X. Goemans
  • Milena Mihail
  • Vijay V. Vazirani
Article

Abstract

We present the first polynomial-time approximation algorithm for finding a minimum-cost subgraph having at least a specified number of edges in each cut. This class of problems includes, among others, the generalized Steiner network problem, also called the survivable network design problem. Ifk is the maximum cut requirement of the problem, our solution comes within a factor of 2k of optimal. Our algorithm is primal-dual and shows the importance of this technique in designing approximation algorithms.

Mathematics Subject Classification (1991)

05 C 40 68 Q 25 90 C 10 90 C 35 

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Copyright information

© Akadémiai Kiadó 1995

Authors and Affiliations

  • David P. Williamson
    • 1
  • Michel X. Goemans
    • 2
  • Milena Mihail
    • 3
  • Vijay V. Vazirani
    • 4
  1. 1.IBM T. J. Watson Research CenterYorktown HeightsUSA
  2. 2.Department of MathematicsMITCambridgeUSA
  3. 3.BellcoreMorristownUSA
  4. 4.Computer Science and Engineering DepartmentIndian Institute of TechnologyNew DelhiIndia

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