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Better algorithms for minimum weight vertex-connectivity problems

  • Vincenzo Auletta
  • Mimmo Parente
Algorithms IV
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1200)

Abstract

Given a k vertex-connected graph with weighted edges, we study the problem of finding a minimum weight spanning subgraph which is k vertex-connected, for small values of k. The problem is known to be NP-hard for any k, even when edges have no weight.

In this paper we provide a 2 approximation algorithm for the cases k=2, 3 and a 3 approximation algorithm for the case k=4. The best approximation factors present in literature are 2, 3 + 2/3 and 4 + 1/6, respectively.

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References

  1. 1.
    B. Bollobás Extremal Graph Theory, Academic Press, London, 1978.Google Scholar
  2. 2.
    Y. Dinitz, Z. Nutov, Finding minimum weight k-vertex connected spanning sub-graphs: approximation algorithms with factor 2 for k=3 and factor 3 for k=4, 5, TR-CS0886, Technion, Israel, 1996. (Also to appear in the proceedings of CIAC '97.)Google Scholar
  3. 3.
    K.P. Eswaran, R.E. Tarjan, Augmentations Problems, SIAM Jour. on Computing, (5), 4, 653–665, (1976).CrossRefGoogle Scholar
  4. 4.
    A. Frank, É. Tardos, An application of Submodular Flows, Linear Algebra and its Applications 114/115, 329–348, (1989).CrossRefGoogle Scholar
  5. 5.
    G. N. Frederickson, J. JáJá, On the relationship between the biconnectivity augmentation and travelling salesman problem Theoretical Computer Science, 19(2), 189–201, (1982).CrossRefGoogle Scholar
  6. 6.
    H. N. Gabow, A representation for Crossing Set Families with Applications to Submodular Flow Problems, in Proc. of Symposium On Discrete Algorithms, SODA '93, 202–211, (1993).Google Scholar
  7. 7.
    M. R. Garey, D.S. Johnson, Computers and Intractability, Freeman, New York, 1979.Google Scholar
  8. 8.
    M. Grötschel, C. Monma, M. Stoer, Design of survivable networks, Handbook in Operations Research and Management Science, Volume on Networks, 1993.Google Scholar
  9. 9.
    S. Khuller, B. Raghavachari, Improved Approximation Algorithms for Uniform Connectivity Problems, in Proc. of Symposium on the Theory of Computing, STOC '95, 1–10, (1995).Google Scholar
  10. 10.
    S. Khuller, R. Thurimella, Approximation Algorithms for Graph Augmentation, J. of Algorithms 14, 214–225, (1993).CrossRefGoogle Scholar
  11. 11.
    M. Penn, H. Shasha-Krupnik, Improved Approximation Algorithms for Weighted 2 & 3 Vertex Connectivity Augmentation Problems, Manuscript. (to appear on J. of Algorithms).Google Scholar
  12. 12.
    R. Ravi, D.P. Williamson, An Approximation Algorithm for Minimum-Cost Vertex-Connectivity Problems, in Proc. of Symposium On Discrete Algorithms, SODA '95, 332–341, (1995).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Vincenzo Auletta
    • 1
  • Mimmo Parente
    • 1
  1. 1.Dipartimento di Informatica ed Applicazioni, “R.M. Capocelli”Università di SalernoBaronissiItaly

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