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

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Abstract

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 We describe these (previously unpublished) enhancements, and present a new computational study wherein we run the current code on the largest problem instances from the 2000-study, and on a number of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.

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Notes

  1. Link to graph instances: http://dimacs11.zib.de/downloads.html.

  2. The GeoSteiner branch-and-cut framework was written in 1995–1998. At that time the CPLEX MIP solver was too primitive to provide good support for user-provided separation algorithms, primal heuristics and other plugins currently taken for granted—so we wrote our own branch-and-cut framework using CPLEX as just an LP solver. This also made it easier to support other LP solvers such as lp_solve.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Computer Science, University of Copenhagen, 2100, Copenhagen Ø, Denmark

    Daniel Juhl, Pawel Winter & Martin Zachariasen

  2. Group W. Inc., 2650 Park Tower Drive, Suite 500, Vienna, VA, 22180, USA

    David M. Warme

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  1. Daniel Juhl
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  2. David M. Warme
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  3. Pawel Winter
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  4. Martin Zachariasen
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Correspondence to Daniel Juhl.

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Juhl, D., Warme, D.M., Winter, P. et al. The GeoSteiner software package for computing Steiner trees in the plane: an updated computational study. Math. Prog. Comp. 10, 487–532 (2018). https://doi.org/10.1007/s12532-018-0135-8

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