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On the Integrality Gap of a Natural Formulation of the Single-sink Buy-at-Bulk Network Design Problem

  • Naveen Garg
  • Rohit Khandekar
  • Goran Konjevod
  • R. Ravi
  • F. S. Salman
  • Amitabh Sinha
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2081)

Abstract

We study two versions of the single sink buy-at-bulk network design problem. We are given a network and a single sink, and several sources which demand a certain amount of flow to be routed to the sink. We are also given a finite set of cable types which have different cost characteristics and obey the principle of economies of scale. We wish to construct a minimum cost network to support the demands, using our given cable types. We study a natural integer program formulation of the problem, and show that its integrality gap is O(k), where k is the number of cable types. As a consequence, we also provide an O(k)-approximation algorithm.

Keywords

Short Path Approximation Algorithm Steiner Tree Network Design Problem Integer Program Formulation 
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.

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References

  1. 1.
    Agrawal, A., Klein, P., Ravi, R.: When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM Journal of Computing, 24(3):440–456, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Althöfer, I., Das, G., Dobkin, D., Joseph, D., Soares, J.: On sparse spanners of weighted graphs. Discrete and Computational Geometry, 9:81–100, 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Andrews, M., Z hang, L.: The access network design problem. Proc. of the 39th Ann. IEEE Symp. on Foundations of Computer Science, 42–49, October 1998.Google Scholar
  4. 4.
    Awerbuch, B., Azar, Y.: Buy at bulk network design. Proc. 38th Ann. IEEE Symposium on Foundations of Computer Science, 542–547, 1997.Google Scholar
  5. 5.
    Bartal, Y.: On approximating arbitrary metrics by tree metrics. Proc. 30th Ann. ACM Symposium on Theory of Computing, 1998.Google Scholar
  6. 6.
    Garg, N., Khandekar, R., Konjevod, G., Ravi, R., Salman, F.S., Sinha, A.: A mathematical formulation of a transportation problem with economies of scale. Carnegie Bosch Institute Working Paper 01–1, 2001.Google Scholar
  7. 7.
    Guha, S., M eyerson, A., Munagala, K.: Improved combinatorial algorithms for single sink edge installation problems. To appear in Proc. 33rd Ann. ACM Symposium on Theory of Computing, 2001.Google Scholar
  8. 8.
    Guha, S., Meyerson, A., Munagala, K.: Heirarchical placement and network design problems. Proc. 41st Ann. IEEE Symposium on Foundations of Computer Sciece, 2000.Google Scholar
  9. 9.
    Hassin, R., R avi, R., Salman, F.S.: Approximation algorithms for a capacitated network design problem. Proc. of the APPROX 2000, 167–176, 2000.Google Scholar
  10. 10.
    Khuller, S., Raghavachari, B., Young, N.E.: Balancing minimum spanning and shortest path trees. Algorithmica, 14, 305–322, 1993.CrossRefMathSciNetGoogle Scholar
  11. 11.
    Mansour, Y., P eleg, D.: An approximation algorithm for minimum-cost network design. The Weizman Institute of Science, Rehovot, 76100 Israel, Tech. Report CS94-22, 1994; Also presented at the DIMACS workshop on Robust Communication Networks, 1998.Google Scholar
  12. 12.
    Meyerson, A., Munagala, K., Plotkin, S.: Cost-distance: Two metric network design. Proc. 41st Ann. IEEE Symposium on Foundations of Computer Science, 2000.Google Scholar
  13. 13.
    Ravi, R., Salman, F.S.: Approximation algorithms for the traveling purchaser problem and its variants in network design. Proc. of the European Symposium on Algorithms, 29–40, 1999.Google Scholar
  14. 14.
    Salman, F.S., Cheriyan, J., Ravi R., Subramanian, S.: Approximating the single sink link-installation problem in network design. SIAM Journal of Optimization 11(3):595–610, 2000.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Naveen Garg
    • 1
  • Rohit Khandekar
    • 1
  • Goran Konjevod
    • 2
  • R. Ravi
    • 3
  • F. S. Salman
    • 4
  • Amitabh Sinha
    • 3
  1. 1.Department of Computer Science and EngineeringIndian Institute of TechnologyNew DelhiIndia
  2. 2.Department of Computer Science and EngineeringArizona State UniversityUSA
  3. 3.GSIACarnegie Mellon UniversityPittsburghUSA
  4. 4.Krannert School of ManagementPurdue UniversityUSA

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