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arXiv · 2112.04343

The Complexity of the Hausdorff Distance

Paul Jungeblut·Linda Kleist·Tillmann Miltzow
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Abstract

We investigate the computational complexity of computing the Hausdorff distance. Specifically, we show that the decision problem of whether the Hausdorff distance of two semi-algebraic sets is bounded by a given threshold is complete for the complexity class $\forall\exists_<\mathbb{R}$. This implies that the problem is NP-, co-NP-, $\exists\mathbb{R}$- and $\forall\mathbb{R}$-hard.

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Paul Jungeblut, Linda Kleist, Tillmann Miltzow. 2021-12-08. The Complexity of the Hausdorff Distance. https://arxiv.org/abs/2112.04343

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