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Numerical Calibration of Steiner trees

  • Annalisa Massaccesi
  • Edouard Oudet
  • Bozhidar Velichkov
Article

Abstract

In this paper we propose a variational approach to the Steiner tree problem, which is based on calibrations in a suitable algebraic environment for polyhedral chains which represent our candidates. This approach turns out to be very efficient from numerical point of view and allows to establish whether a given Steiner tree is optimal. Several examples are provided.

Keywords

Calibration Minimal surface Steiner tree problem 

Mathematics Subject Classification

49J45 35R35 49M05 35J25 

Notes

Acknowledgements

We would like to thank the MmgTools team (see https://github.com/MmgTools/mmg): Charles Dapogny, Cécile Dobrzynski, Pascal Frey and Algiane Froehly) for providing the remeshing software required to generate constraint meshes. Édouard Oudet gratefully acknowledges the support of the ANR, through the projects COMEDIC, GEOMETRYA, PGMO and OPTIFORM.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Annalisa Massaccesi
    • 1
  • Edouard Oudet
    • 2
  • Bozhidar Velichkov
    • 2
  1. 1.Institut für MathematiUniversität ZürichZürichSwitzerland
  2. 2.Laboratoire Jean Kuntzmann (LJK)Université Grenoble AlpesSaint-Martin-d’HèresFrance

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