Advertisement

Abstract

We consider a single source network design problem from a game-theoretic perspective. Gupta, Kumar and Roughgarden (Proc. 35th Annual ACM STOC, pages 365–372, 2003) developed a simple method for single source rent-or-buy problem that also yields the best-known approximation ratio for the problem. We show how to use a variant of this method to develop an approximately budget-balanced and group strategyproof cost-sharing method for the problem.

The novelty of our approach stems from our obtaining the cost-sharing methods for the rent-or-buy problem by carefully combining cost-shares for the simpler problem Steiner tree problem; we feel that this idea may have wider implications. Our algorithm is conceptually simpler than the previous such cost-sharing method due to Pál and Tardos (Proc. 44th Annual FOCS, pages 584–593, 2003), and has a much improved approximation factor of 4.6 (over the previously known factor of 15).

Keywords

Network Design Steiner Tree Network Design Problem Connection Cost Indicator Random Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bellare, M., Rompel, J.: Randomness-efficient oblivious sampling. In: Proc. 35th FOCS, pp. 276–287 (1994)Google Scholar
  2. 2.
    Even, G., Goldreich, O., Luby, M., Nisan, N., Veličković, B.: Approximations of general independent distributions. In: Proc. 24th STOC, pp. 10–16 (1992)Google Scholar
  3. 3.
    Gupta, A., Kumar, A., Kleinberg, J., Rastogi, R., Yener, B.: Provisioning a Virtual Private Network: A network design problem for multicommodity flow. In: Proc. 33rd STOC, pp. 389–398 (2001)Google Scholar
  4. 4.
    Gupta, A., Kumar, A., Roughgarden, T.: Simpler and better approximation algorithms for network design. In: 35th STOC, pp. 365–372 (2003)Google Scholar
  5. 5.
    Kent, K.J., Skorin-Kapov, D.: Population monotonic cost allocations on MSTs. In: Proceedings of the 6th International Conference on Operational Research, Rovinj, 1996 pp. 43–48 (1996)Google Scholar
  6. 6.
    Moulin, H., Shenker, S.: Strategyproof sharing of submodular costs: budget balance versus efficiency. Economic Theor. 18, 511–533 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Jain, K., Vazirani, V.: Applications of approximation algorithms to cooperative games. In: Proc. 33rd STOC, pp. 364–372 (2001)Google Scholar
  8. 8.
    Karger, D.R., Minkoff, M.: Building Steiner trees with incomplete global knowledge. In: Proc. 41th FOCS, pp. 613–623 (2000)Google Scholar
  9. 9.
    Pál, M., Tardos, É.: Group Strategyproof Mechanisms via Primal-Dual Algorithms. In: Proc. 44th FOCS, pp. 584–593 (2003)Google Scholar
  10. 10.
    Robins, G., Zelikovsky, A.: Improved Steiner tree approximation in graphs. In: Proc. 11th SODA, pp. 770–779 (2000)Google Scholar
  11. 11.
    Schmidt, J.P., Siegel, A., Srinivasan, A.: Chernoff-Hoeffding bounds for applications with limited independence. SIAM J. Discrete Math. 8, 223–250 (1995)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Anupam Gupta
    • 1
  • Aravind Srinivasan
    • 2
  • Éva Tardos
    • 3
  1. 1.Department of Computer ScienceCarnegie Mellon UniversityPittsburghUSA
  2. 2.Department of Computer Science and, University of Maryland Institute for Advanced Computer StudiesUniversity of Maryland at College ParkCollege ParkUSA
  3. 3.Department of Computer ScienceCornell UniversityIthacaUSA

Personalised recommendations