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arXiv · 1401.1434

Computational Aspects of the Hausdorff Distance in Unbounded Dimension

Stefan König
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Abstract

We study the computational complexity of determining the Hausdorff distance of two polytopes given in halfspace- or vertex-presentation in arbitrary dimension. Subsequently, a matching problem is investigated where a convex body is allowed to be homothetically 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.

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Stefan König. 2014-01-07. Computational Aspects of the Hausdorff Distance in Unbounded Dimension. https://arxiv.org/abs/1401.1434

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