Approximation Algorithms for a Capacitated Network Design Problem

  • R. Hassin
  • R. Ravi
  • F. S. Salman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1913)


We study a network loading problem with applications in local access network design. Given a network, the problem is to route flow from several sources to a sink and to install capacity on the edges to support flows at minimum cost. Capacity can be purchased only in multiples of a fixed quantity. All the flow from a source must be routed in a single path to the sink. This NP-hard problem generalizes the Steiner tree problem and also more effectively models the applications traditionally formulated as capacitated tree problems. We present an approximation algorithm with performance ratio (ρST+2) where ρST is the performance ratio of any approximation algorithm for minimum Steiner tree. When all sources have the same demand value, the ratio improves to (nST +1) and in particular, to 2 when all nodes in the graph are sources.


Approximation Algorithm Source Node Sink Node Steiner Tree Network Design Problem 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. AG88.
    K. Altinkemer and B. Gavish, “Heuristics with constant error guarantees for the design of tree networks,” Management Science, 34, (1988) 331–341zbMATHMathSciNetCrossRefGoogle Scholar
  2. AZ98.
    M. Andrews and L. Zhang, “The access network design problem,” In Proc. of the 39th Ann. IEEE Symp. on Foundations of Computer Science, (1998) 42–49Google Scholar
  3. CL83.
    K. M. Chandy and T. Lo, “The capacitated minimum tree,” Networks, 3, (1973) 173–182zbMATHCrossRefMathSciNetGoogle Scholar
  4. KR98.
    Kawatra, R. and D. L. Bricker, “A multiperiod planning model for the capacitated minimal spanning tree problem”, to appear in European Journal of Operational Research (1998)Google Scholar
  5. KB83.
    A. Kershenbaumand R. Boorstyn, “Centralized teleprocessing network design,” Networks, 13, (1983) 279–293CrossRefMathSciNetGoogle Scholar
  6. KRY 93.
    S. Khuller, B. Raghavachari and N. E. Young, “Balancing minimum spanning and shortest path trees,” Algorithmica, 14, (1993) 305–322CrossRefMathSciNetGoogle Scholar
  7. MP 94.
    Y. Mansour and D. Peleg, “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
  8. Pap78.
    C. H. Papadimitriou, “The complexity of the capacitated tree problem,” Networks, 8, (1978) 217–230Google Scholar
  9. RZ00.
    G. Robins and A. Zelikovsky, “Improved steiner tree approximation in graphs”, Proc. of the 10th Ann. ACM-SIAM Symp. on Discrete Algorithms, (2000) 770–779Google Scholar
  10. SCR+97.
    F.S. Salman, J. Cheriyan, R. Ravi and S. Subramanian, “Buy-at-bulk network design: Approximating the single-sink edge installation problem,” Proc. of the 8th Ann. ACM-SIAM Symposium on Discrete Algorithms, (1997) 619–628Google Scholar
  11. S83.
    R. L. Sharma, “Design of an economical multidrop network topology with capacity constraints,” IEEE Trans. Comm., 31, (1983) 590–591CrossRefGoogle Scholar
  12. SS99.
    B. Sanso and P. Soriano, Editors, “Telecommunications Network Planning,” Kluwer Academic Publishers, 1999.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • R. Hassin
    • 1
  • R. Ravi
    • 2
  • F. S. Salman
    • 2
  1. 1.Department of Statistics and Operations ResearchTel-Aviv UniversityIsrael
  2. 2.GSIACarnegie Mellon UniversityPittsburgh

Personalised recommendations