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Computational Aspects of the Hausdorff Distance in Unbounded Dimension

Name: Computational Aspects of the Hausdorff Distance in Unbounded Dimension
Creator: Stefan König
Keywords: Computational Geometry (cs.CG), FOS: Computer and information sciences, QA299.6-433, Metric Geometry (math.MG), 0102 computer and information sciences, 02 engineering and technology, Computational Complexity (cs.CC), 16. Peace & justice, 01 natural sciences, QA76.75-76.765

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2014Embargo end date: 01 Jan 2014Publisher:arXivJournal:Journal of Computational Geometry (issn: 1920-180X,

Authors: Stefan König;

doi: 10.48550/arxiv.1401.1434 , 10.20382/jocg.v5i1a12

arXiv: http://arxiv.org/abs/1401.1434

Computational Aspects of the Hausdorff Distance in Unbounded Dimension

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Abstract

We study the computational complexity of determining the Hausdorff distance oftwo polytopes given in halfspace- or vertex-presentation in arbitrary dimension. Sub-sequently, a matching problem is investigated where a convex body is allowed to behomothetically transformed in order to minimize its Hausdorff distance to another one. For this problem, we characterize optimal solutions, deduce a Helly-type theorem and give polynomial time (approximation) algorithms for polytopes.

Journal of Computational Geometry, Vol. 5 No. 1 (2014)

Related Organizations

Hamburg University of Technology
Germany

Keywords

Computational Geometry (cs.CG), FOS: Computer and information sciences, QA299.6-433, Metric Geometry (math.MG), Computational Complexity (cs.CC), QA76.75-76.765, Computer Science - Computational Complexity, Mathematics - Metric Geometry, FOS: Mathematics, Computer Science - Computational Geometry, Computer software, Analysis

1 Research products, page 1 of 1

Journal of Computational Geometry, Vol. 5 No. 1 (2014)
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