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Parallel Algorithms and Architectures pp 176–183Cite as

Computing a rectilinear steiner minimal tree in \(n^{O(\sqrt n )}\)time

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 269))

Abstract

We propose an algorithm for computing a rectilinear Steiner minimal tree on n points in \(2^{O(\sqrt n \log n)}\)time and O(n 2) space. This is an asymptotic improvement on the 2O(n) time required by current algorithms. If the points are distributed uniformly at random on the unit square, the Steiner tree calculated by our algorithm is minimal with high probability. The “constant factors” of our algorithm are such that it should be feasible to obtain exact solutions for n-point problems whenever n≤25. Previously, only problems of size n≤20 were feasible.

Supported by the National Science Foundation, through its Design, Tools and Test Program under grant number MIP 84-06408.

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Authors and Affiliations

  1. Computer Science Department, University of Minnesota, 55812, Duluth, Minnesota, U.S.A.

    Clark D. Thomborson (a.k.a. Thompson), Linda L. Deneen & Gary M. Shute

Authors
  1. Clark D. Thomborson (a.k.a. Thompson)
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  2. Linda L. Deneen
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  3. Gary M. Shute
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Andreas Albrecht Hermann Jung Kurt Mehlhorn

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© 1987 Springer-Verlag Berlin Heidelberg

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Thomborson (a.k.a. Thompson), C.D., Deneen, L.L., Shute, G.M. (1987). Computing a rectilinear steiner minimal tree in \(n^{O(\sqrt n )}\)time. In: Albrecht, A., Jung, H., Mehlhorn, K. (eds) Parallel Algorithms and Architectures. Lecture Notes in Computer Science, vol 269. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18099-0_44

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  • DOI: https://doi.org/10.1007/3-540-18099-0_44

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18099-9

  • Online ISBN: 978-3-540-47760-0

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