The Steiner tree problem revisited through rectifiable G-currents

The Steiner tree problem can be stated in terms of finding a connected set of minimal length containing a given set of finitely many points. We show how to formulate it as a mass-minimization problem for 1-dimensional currents with coefficients in a suitable normed group. The representation used for...

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Bibliographic Details
Published inAdvances in calculus of variations Vol. 9; no. 1; pp. 19 - 39
Main Authors Marchese, Andrea, Massaccesi, Annalisa
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.01.2016
Walter de Gruyter GmbH
Subjects
49Q15
49Q20
Calculus of variations
Calibration
chains
Decision trees
flat
Mathematical analysis
Optimization
rectifiable currents
Representations
Steiner tree problem
Trees
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Summary:The Steiner tree problem can be stated in terms of finding a connected set of minimal length containing a given set of finitely many points. We show how to formulate it as a mass-minimization problem for 1-dimensional currents with coefficients in a suitable normed group. The representation used for these currents allows to state a calibration principle for this problem. We also exhibit calibrations in some examples.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1864-8258
1864-8266
DOI:10.1515/acv-2014-0022