Numerical Calibration of Steiner trees

Article, Preprint English OPEN
Massaccesi , Annalisa; Oudet , Edouard; Velichkov , Bozhidar;
(2016)
  • Publisher: Springer Verlag (Germany)
  • Related identifiers: doi: 10.1007/s00245-017-9421-5
  • Subject: Steiner tree problem | Minimal surface | [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] | [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] | [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA] | 35R35, 49M05, 35J25, 49J45 | [ MATH.MATH-DG ] Mathematics [math]/Differential Geometry [math.DG] | Calibration
    arxiv: Mathematics::Metric Geometry | Computer Science::Computational Geometry

International audience; 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 fro... View more
  • References (8)

    [1] Chambolle, Antonin and Pock, Thomas, A rst-order primal-dual algorithm for convex problems with applications to imaging, Journal of Mathematical Imaging and Vision, 40.1, (2011), 120{145.

    [2] Federer, Herbert, Geometric measure theory, (Springer-Verlag New York Inc., New York), (1969).

    [3] Gilbert, Edgar N. and Pollak, Henry O., Steiner minimal trees, SIAM Journal on Applied Mathematics, 16, (1968), 1{29.

    [4] Ivanov, Alexandr O. and Tuzhilin, Alexei A., Minimal networks. The Steiner problem and its generalizations (CRC Press, Boca Raton, FL), (1994).

    [5] Karp, Richard M., Reducibility among combinatorial problems, Complexity of computer computations (Proc. Sympos., IBM Thomas J. Watson Res. Center, Yorktown Heights, N.Y., 1972), (1972), 85{103.

    [6] Marchese, Andrea and Massaccesi, Annalisa, The Steiner tree problem revisited through recti able G-currents, Advances in Calculus of Variations, 9.1, (2016), 19{39.

    [7] Raguet, Hugo and Fadili, Jalal and Peyre, Gabriel, A generalized forward-backward splitting, SIAM Journal on Imaging Sciences, 6.3, (2013), 1199{1226.

    [8] Warme, DM and Winter, P and Zachariasen, M, GeoSteiner 3.1, Department of Computer Science, University of Copenhagen (DIKU), (2001).

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