Archive for History of Exact Sciences

, Volume 68, Issue 3, pp 327–354 | Cite as

On the history of the Euclidean Steiner tree problem

  • Marcus BrazilEmail author
  • Ronald L. Graham
  • Doreen A. Thomas
  • Martin Zachariasen


The history of the Euclidean Steiner tree problem, which is the problem of constructing a shortest possible network interconnecting a set of given points in the Euclidean plane, goes back to Gergonne in the early nineteenth century. We present a detailed account of the mathematical contributions of some of the earliest papers on the Euclidean Steiner tree problem. Furthermore, we link these initial contributions with results from the recent literature on the problem.


Fermat Minimum Span Tree Equilateral Triangle Steiner Tree Steiner Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Two of the authors, Marcus Brazil and Doreen Thomas, were partially supported in the writing of this paper by a grant from the Australian Research Council. We would also like to thank: Francois Lauze (University of Copenhagen) and Morgan Tort (The University of Melbourne) for their generous assistance with the French translations required for this paper; Henry Pollak for useful commentary on Gauss’ letters; Pavol Hell (Simon Fraser University) for assistance with translating (Jarník and Kössler 1934); Jakob Krarup (University of Copenhagen) for help with providing some original sources; Donald Knuth for helpful comments and suggestions on an earlier draft of this paper; and Konrad Swanepoel for alerting us to the existence of the paper of Menger (1931).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Marcus Brazil
    • 1
    Email author
  • Ronald L. Graham
    • 2
  • Doreen A. Thomas
    • 3
  • Martin Zachariasen
    • 4
  1. 1.Department of Electrical and Electronic EngineeringThe University of MelbourneMelbourneAustralia
  2. 2.Department of Computer Science and EngineeringUC San DiegoLa JollaUSA
  3. 3.Department of Mechanical EngineeringThe University of MelbourneMelbourneAustralia
  4. 4.Department of Computer ScienceUniversity of CopenhagenCopenhagen ØDenmark

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