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The Steiner Ratio of L p -planes

  • Chapter
Handbook of Combinatorial Optimization

Abstract

Starting with the famous book ”What is Mathematics” by Courant and Robbins the following problem has been popularized under the name of Steiner: For a given finite set of points in a metric space find a network which connects all points of the set with minimal length. Such a network must be a tree, which is called a Steiner Minimal Tree (SMT). It may contain vertices other than the points which are to be connected. Such points are called Steiner points.1 A classical survey of this problem in the Euclidean plane was given by Gilbert and Pollak [23]. An updated one can be found in [27].

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, University of Greifswald, Germany

    Jens Albrecht & Dietmar Cieslik

Authors
  1. Jens Albrecht
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  2. Dietmar Cieslik
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Minnesota, USA

    Ding-Zhu Du

  2. Institute of Applied Mathematics, Academia Sinica, P. R. China

    Ding-Zhu Du

  3. Department of Industrial and Systems Engineering, University of Florida, USA

    Panos M. Pardalos

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© 1999 Springer Science+Business Media Dordrecht

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Albrecht, J., Cieslik, D. (1999). The Steiner Ratio of L p -planes. In: Du, DZ., Pardalos, P.M. (eds) Handbook of Combinatorial Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3023-4_8

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  • DOI: https://doi.org/10.1007/978-1-4757-3023-4_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4813-7

  • Online ISBN: 978-1-4757-3023-4

  • eBook Packages: Springer Book Archive

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