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

  • Clark D. Thomborson (a.k.a. Thompson)
  • Linda L. Deneen
  • Gary M. Shute
Invited Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 269)


We propose an algorithm for computing a rectilinear Steiner minimal tree on n points in \(2^{O(\sqrt n \log n)}\)time and O(n2) 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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Clark D. Thomborson (a.k.a. Thompson)
    • 1
  • Linda L. Deneen
    • 1
  • Gary M. Shute
    • 1
  1. 1.Computer Science DepartmentUniversity of MinnesotaDuluthU.S.A.

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