Mathematical Programming Computation

, Volume 10, Issue 4, pp 487–532 | Cite as

The GeoSteiner software package for computing Steiner trees in the plane: an updated computational study

  • Daniel JuhlEmail author
  • David M. Warme
  • Pawel Winter
  • Martin Zachariasen
Full Length Paper


The GeoSteiner software package has for about 20 years been the fastest (publicly available) program for computing exact solutions to Steiner tree problems in the plane. The computational study by Warme, Winter and Zachariasen, published in 2000, documented the performance of the GeoSteiner approach—allowing the exact solution of Steiner tree problems with more than a thousand terminals. Since then, a number of algorithmic enhancements have improved the performance of the software package significantly. We describe these (previously unpublished) enhancements, and present a new computational study wherein we run the current code on the largest problem instances from the 2000-study, and on a number of larger problem instances. The computational study is performed using the commercial GeoSteiner 4.0 code base, and the performance is compared to the publicly available GeoSteiner 3.1 code base as well as the code base from the 2000-study. The software studied in the paper is being released as GeoSteiner 5.0 under an open source license.


Euclidean Steiner tree problem Rectilinear Steiner tree problem Fixed orientation Steiner tree problem Exact algorithm Computational study 

Mathematics Subject Classification

90C10 Integer programming 90C27 Combinatorial optimization 05C05 Trees 05C65 Hypergraphs 51N20 Euclidean analytic geometry 68W35 VLSI algorithms 



The authors would like to thank the referees for their comments that helped to improve this paper.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and The Mathematical Programming Society 2018

Authors and Affiliations

  • Daniel Juhl
    • 1
    Email author
  • David M. Warme
    • 2
  • Pawel Winter
    • 1
  • Martin Zachariasen
    • 1
  1. 1.Department of Computer ScienceUniversity of CopenhagenCopenhagen ØDenmark
  2. 2.Group W. Inc.ViennaUSA

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