Computational Aspects of the Hausdorff Distance in Unbounded Dimension
Computational Geometry
2014-01-08 v1 Computational Complexity
Metric Geometry
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.
Keywords
Cite
@article{arxiv.1401.1434,
title = {Computational Aspects of the Hausdorff Distance in Unbounded Dimension},
author = {Stefan König},
journal= {arXiv preprint arXiv:1401.1434},
year = {2014}
}