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Finding k-Connected Subgraphs with Minimum Average Weight

  • Prabhakar Gubbala
  • Balaji Raghavachari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)

Abstract

We consider the problems of finding k-connected spanning subgraphs with minimum average weight. We show that the problems are NP-hard for k>1. Approximation algorithms are given for four versions of the minimum average edge weight problem:
  1. 1

    3-approximation for k-edge-connectivity,

     
  2. 2

    O(logk) approximation for k-node-connectivity

     
  3. 3

    2+ ε approximation for k-node-connectivity in Euclidian graphs, for any constant ε> 0,

     
  4. 4

    5.8-approximation for k-node-connectivity in graphs satisfying the triangle inequality.

     

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References

  1. 1.
    Cheriyan, J., Thurimella, R.: Approximating minimum-size k-connected spanning subgraphs via Matching. SIAM J. Comput. 30, 528–560 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Cheriyan, J., Vempala, S., Vetta, A.: Approximation algorithms for minimum-cost k-vertex connected subgraphs. In: STOC 2002, pp. 306–312 (2002)Google Scholar
  3. 3.
    Fernandes, C.G.: A better approximation for the minimum k-edge-connected spanning subgraph problem. J. Algorithms 28, 105–124 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Frederickson, G.N., JáJá, J.: Approximation algorithms for several graph augmentation problems. SIAM J. Comput. 5, 25–53 (1982)Google Scholar
  5. 5.
    Khuller, S., Vishkin, U.: Biconnectivity approximations and graph carvings. J. Assoc. Comput. Mach. 41, 214–235 (1994)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Czumaj, A., Lingas, A.: A Polynomial Time Approximation Scheme for Euclidean Minimum Cost k-Connectivity. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 682–694. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  7. 7.
    Czumaj, A., Lingas, A.: On Approximability of the Minimum-Cost k-Connected Spanning Subgraph Problem. In: Proc. 10th Annual ACM-SIAM Symp. on Discrete. Algoithms (SODA), pp. 281–290 (1999)Google Scholar
  8. 8.
    Karp, R.M.: A characterization of the minimum cycle mean in a digraph. Discrete Math. 23, 309–311 (1978)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Ahuja, R.K., Orlin, J.B.: New scaling algorithms for assignment and minimum cycle mean problems. Mathematical Programming 54, 41–56 (1992)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Prabhakar Gubbala
    • 1
  • Balaji Raghavachari
    • 1
  1. 1.Computer Science DepartmentUniversity of Texas at DallasRichardson

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