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Optimal rectilinear steiner tree for extremal point sets

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Algorithms and Computation (ISAAC 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 762))

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Abstract

We present an O(n3)-time algorithm to construct an optimal rectilinear Steiner tree for an extremal point set of size n. Our result subsumes those given in [1, 4] and it partially improves on the result in [5].

Part of the work was done while the authors were at University of Minnesota, Department of Computer Science. Work on this paper by the first author was partially supported by RGC grant DAG92/93.EG09.

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References

  1. M. Bern. Faster exact algorithms for Steiner trees in planar networks. Networks, 20:109–120, 1990.

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  2. S.W. Cheng, Andrew Lim, and C.T. Wu. Optimal rectilinear steiner tree for extremal point set. Technical Report Technical Report HKUST-CS93-6, HKUST, Department of Computer Science, April 1993.

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  3. J.P. Cohoon, D.S. Richards, and J.S. Salowe. An optimal steiner tree algorithm for a net whose terminals lie on the perimeter of a rectangle. IEEE Transactions On Computer-Aided Design, 9(4):398–407, 1990.

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  4. J.S. Provan. Convexity and the steiner tree problem. Networks, 18:55–72, 1988.

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  5. D.S. Richard and J.S. Salowe. A linear-time algorithm to construct a rectilinear Steiner minimal tree for k-extremal point sets. Algorithmica, 7:247–276, 1992.

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Author information

Authors and Affiliations

  1. Department of Computer Science, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong

    Siu-Wing Cheng

  2. Information Technology Institute, National Computer Board, 71 Science Park Drive, Republic of Singapore

    Andrew Lim

  3. 55144, 3M, St. Paul, Minnesota, USA

    Ching-Ting Wu

Authors
  1. Siu-Wing Cheng
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  2. Andrew Lim
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  3. Ching-Ting Wu
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Editor information

K. W. Ng P. Raghavan N. V. Balasubramanian F. Y. L. Chin

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© 1993 Springer-Verlag Berlin Heidelberg

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Cheng, SW., Lim, A., Wu, CT. (1993). Optimal rectilinear steiner tree for extremal point sets. In: Ng, K.W., Raghavan, P., Balasubramanian, N.V., Chin, F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57568-5_284

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  • DOI: https://doi.org/10.1007/3-540-57568-5_284

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57568-9

  • Online ISBN: 978-3-540-48233-8

  • eBook Packages: Springer Book Archive

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