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The Euclidean Bottleneck Steiner Tree and Steiner Tree with Minimum Number of Steiner Points

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Computing and Combinatorics (COCOON 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2108))

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Abstract

We study variations of Steiner tree problem. Let P = ·p1, p2, ...,p n× be a set of n terminals in the Euclidean plane. For a positive integer k, the bottleneck Steiner tree problem (BSTP for short) is to find a Steiner tree with at most k Steiner points such that the length of the longest edges in the tree is minimized. For a positive constant R, the Steiner tree problem with minimum number of Steiner points (STP - MSP for short) asks for a Steiner tree such that each edge in the tree has length at most R and the number of Steiner points is minimized.In this paper, we give (1) a ratio-\( \sqrt 3 + \varepsilon \) approximation algorithm for BSTP, where € is an arbitrary positive number(2) a ratio-3 approximation algorithm for STP-MSP with running time O(n 3);(3)a ratio-52 approximation algorithm for STP-MSP

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References

  1. D. Chen, D.-Z. Du, X.. Hu, G. Lin, L. Wang and G. Xue, “Approximations for Steiner trees with minimum number of Steiner points”, Journal of Global Optimization, vol. 18, pp. 17–33, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  2. C. Chiang, M. Sarrafzadeh and C.K. Wong, “A powerful global router: based on Steiner min-max tree”, IEEE Transactions on Computer-Aided Design, 19, pp. 1318–1325, 1990.

    Article  Google Scholar 

  3. C.-S. Li, F.F. Tong, C.J. Georgiou and M. Chen, Gain equalization in metropolitan and wide area optical networks using optical amplifiers, Proc. IEEE INFOCOM’94, pp. 130–137, June 1994.

    Google Scholar 

  4. G. Lin and G. Xue, “Steiner tree problem with minimum number of Steiner points and bounded edge-length”, Information ProcessingL etters, 69, pp. 53–57, 1999.

    Article  MathSciNet  Google Scholar 

  5. B. Ramamurthy, J. Iness and B. Mukherjee, Minimizing the number of optical amplifiers needed to support a multi-wavelength optical LAN/MAN, Proc. IEEE INFOCOM’97, pp. 261–268, April 1997.

    Google Scholar 

  6. H.J. Prömel and A. Steger, “A NewAppro ximation Algorithm for the Steiner Tree Problem with Performance Ratio 5/3”, Journal of Algorithms, 36, pp. 89–101, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Sarrafzadeh and C.K. Wong, “Bottleneck Steiner trees in the plane”, IEEE Transactions on Computers, 41, pp. 370–374, 1992.

    Article  MathSciNet  Google Scholar 

  8. L. Wang and D.-Z. Du, “Approximations for a Bottleneck Steiner Tree Problem”, Algorithmica, to appear.

    Google Scholar 

  9. L. wang and Z. Li, “An Approximation Algorithm for a Bottleneck Steiner Tree Problem in the Euclidean Plane”, Information ProcessingL etters, to appear.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Minnesota, Minnesota, MN, 55455, USA

    Dingzhu Du

  2. Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong

    Lusheng Wang

  3. Institute of Systems Sciences, Academy of Math. & Systems Sciences, Beijing, 100080

    Baogang Xu

Authors
  1. Dingzhu Du
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  2. Lusheng Wang
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  3. Baogang Xu
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Massachusetts, One University Avenue, Lowell, MA, 01854, USA

    Jie Wang

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© 2001 Springer-Verlag Berlin Heidelberg

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Du, D., Wang, L., Xu, B. (2001). The Euclidean Bottleneck Steiner Tree and Steiner Tree with Minimum Number of Steiner Points. In: Wang, J. (eds) Computing and Combinatorics. COCOON 2001. Lecture Notes in Computer Science, vol 2108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44679-6_57

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  • DOI: https://doi.org/10.1007/3-540-44679-6_57

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42494-9

  • Online ISBN: 978-3-540-44679-8

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