The (K,k)-Capacitated Spanning Tree Problem

  • Esther M. Arkin
  • Nili Guttmann-Beck
  • Refael Hassin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6124)

Abstract

This paper considers a generalization of the capacitated spanning tree, in which some of the nodes have capacity K, and the others have capacity k < K. We prove that the problem can be approximated within a constant factor, and present better approximations when k is 1 or 2.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Altinkemer, K., Gavish, B.: Heuristics with constant error guarantees for the design of tree networks. Management Sci. 34, 331–341 (1988)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Deo, N., Kumar, N.: Computation of constrained spanning trees: a unified approach. Lecture Notes in Econ. and Math. Systems, vol. 450, pp. 194–220. Springer, Berlin (1997)Google Scholar
  3. 3.
    Gamvros, I., Raghavan, S., Golden, B.: An evolutionary approach to the multi-level Capacitated Minimum Spanning Tree problem. Technical report (2002)Google Scholar
  4. 4.
    Gavish, B.: Formulations and algorithms for the capacitated minimal directed tree problem. J. Assoc. Comput. Mach. 30, 118–132 (1983)MATHMathSciNetGoogle Scholar
  5. 5.
    Gavish, B.: Topological design of telecommunication networks - local access design methods. Annals of Operations Research 33, 17–71 (1991)MATHCrossRefGoogle Scholar
  6. 6.
    Gavish, B., Li, C.L., Simchi-Levi, D.: Analysis of heuristics for the design of tree networks. Annals of Operations Research 36, 77–86 (1992)MATHCrossRefGoogle Scholar
  7. 7.
    Gouveia, L., Lopes, M.J.: Using generalized capacitated trees for designing the topology of local access networks. Telecommunication Systems 7, 315–337 (1997)CrossRefGoogle Scholar
  8. 8.
    Jothi, R., Raghavachari, B.: Survivable network design: the capacitated minimum spanning network problem. Inform. Process. Let. 91, 183–190 (2004)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Jothi, R., Raghavachari, B.: Approximation algorithms for the capacitated minimum spanning tree problem and its variants in network design. ACM Trans. Algorithms 1, 265–282 (2005)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Könemann, J., Ravi, R.: Primal-dual meets local search: approximating MSTs with nonuniform degree bounds. SIAM J. Comput. 34, 763–773 (2005)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Morsy, E., Nagamochi, H.: An improved approximation algorithm for capacitated multicast routings in networks. Theoretical Comput. Sci. 390, 81–91 (2008)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Papadimitriou, C.H.: The complexity of the capacitated tree problem. Networks 8, 217–230 (1978)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Esther M. Arkin
    • 1
  • Nili Guttmann-Beck
    • 2
  • Refael Hassin
    • 3
  1. 1.Department of Applied Mathematics and StatisticsState University of New YorkStony BrookUSA
  2. 2.Department of Computer ScienceThe Academic College of Tel-Aviv YaffoYaffoIsrael
  3. 3.School of Mathematical SciencesTel-Aviv UniversityTel-AvivIsrael

Personalised recommendations