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(1 + ρ)-Approximation for Selected-Internal Steiner Minimum Tree

  • Xianyue Li
  • Yaochun Huang
  • Feng Zou
  • Donghyun Kim
  • Weili Wu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)

Abstract

Selected-internal Steiner minimum tree problem is a generalization of original Steiner minimum tree problem. Given a weighted complete graph G = (V,E) with weight function c, and two subsets \(R^{'}\subsetneq R\subseteq V\) with |R − R | ≥ 2, selected-internal Steiner minimum tree problem is to find a Steiner minimum tree T of G spanning R such that any leaf of T does not belong to R . In this paper, suppose c is metric, we obtain a (1 + ρ)-approximation algorithm for this problem, where ρ is the best-known approximation ratio for the Steiner minimum tree problem.

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References

  1. 1.
    Borchers, A., Du, D.Z.: The k-Steiner Ratio in Graphs. SIAM Journal on Computing 26(3), 857–869 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Cheng, X., Du, D.Z.: Steiner Trees in Industry. Kluwer Academic Publishers, Dordrecht, Netherlands (2001)Google Scholar
  3. 3.
    Du, D.Z.: On Component-Size Bounded Steiner Trees. Discrete Applied Mathematics 60, 131–140 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Du, D.Z., Smith, J.M., Rubinstein, J.H.: Advance in Steriner Tree. Kluwer Academic Publishers, Dordrecht, Netherlands (2000)Google Scholar
  5. 5.
    Foulds, L., Graham, R.: The Steiner Problem in Phylogeny is NP-complete. Advances in Applied Mathematics 3, 43–49 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Garey, M., Graham, R., Johnson, D.: The Complexity of Computing Steriner Minimal Tree. SIAM Journal on Applied Mathematics 32, 835–859 (1997)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Garey, M., Johnson, D.: The Rectilinear Steiner Problem is NP-complete. SIAM Journal on Applied Mathematics 32, 826–834 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Graur, D., Li, W.H.: Fundamentals of Molecular Evolution, 2nd edn. Sinauer Publishers, Sunderland, Massachusetts (2000)Google Scholar
  9. 9.
    Hsieh, S.Y., Yang, S.C.: Approximating the Selected-Internal Steriner Tree. Theoretical Computer Science 381, 288–291 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Hwang, F.K., Richards, D.S., Winter, P.: The Steiner Tree Problem. North-Holland, Amsterdam (1992)zbMATHGoogle Scholar
  11. 11.
    Kahng, A.B., Robins, G.: On Optimal Interconnections for VLSI. Kluwer Publishers, Dordrecht (1995)zbMATHGoogle Scholar
  12. 12.
    Korte, B., Prömel, H.J., Steger, A.: Steiner Trees in VLSI-Layouts. In: Korte, et al. (eds.) Paths, Flows and VLSI-Layout. Springer, Heidelberg (1990)Google Scholar
  13. 13.
    Lu, C.L., Tang, C.Y., Lee, R.C.T.: The Full Steiner Tree Problem. Theoretical Computer Science 306, 55–67 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Robins, G., Zelikovsky, A.: Improved Steiner Tree Approximation in Graphs. In: Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 770–779 (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Xianyue Li
    • 1
  • Yaochun Huang
    • 2
  • Feng Zou
    • 2
  • Donghyun Kim
    • 2
  • Weili Wu
    • 2
  1. 1.School of Mathematics and StatisticsLanzhou UniversityLanzhouP.R. China
  2. 2.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA

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