Numerical calibration of Steiner trees

DOI10.1007/s00245-017-9421-5zbMath1448.49003OpenAlexW2340453700MaRDI QIDQ1734283

Bozhidar Velichkov, Annalisa Massaccesi, Edouard Oudet

Publication date: 27 March 2019

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: http://hal.univ-grenoble-alpes.fr/hal-01304644/file/num_calibration.pdf

zbMATH Keywords

minimal surfaceSteiner tree problemcalibration

Mathematics Subject Classification ID

Trees (05C05) Extremal problems in graph theory (05C35) Numerical methods based on necessary conditions (49M05) Boundary value problems for second-order elliptic equations (35J25) Steiner systems in finite geometry (51E10) Optimization of shapes other than minimal surfaces (49Q10) Free boundary problems for PDEs (35R35) Existence theories for free problems in one independent variable (49J05)

Related Items (11)

Variational Approximation of Functionals Defined on 1-dimensional Connected Sets: The Planar Case ⋮ A convex approach to the Gilbert-Steiner problem ⋮ Minimizing properties of networks via global and local calibrations ⋮ The oriented mailing problem and its convex relaxation ⋮ Energy minimizing maps with prescribed singularities and Gilbert-Steiner optimal networks ⋮ Improved stability of optimal traffic paths ⋮ Calibrations for minimal networks in a covering space setting ⋮ Variational approximation of functionals defined on \(1\)-dimensional connected sets in \(\mathbb{R}^n\) ⋮ Convex Relaxation of Discrete Vector-Valued Optimization Problems ⋮ Stability for the mailing problem ⋮ A Multimaterial Transport Problem and its Convex Relaxation via Rectifiable $G$-currents

Uses Software

• GeoSteiner

Cites Work

• The Steiner tree problem revisited through rectifiable \(G\)-currents
• A first-order primal-dual algorithm for convex problems with applications to imaging
• Reducibility among Combinatorial Problems
• Steiner Minimal Trees
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