License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2022.48
URN: urn:nbn:de:0030-drops-160567
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16056/
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Jungeblut, Paul ; Kleist, Linda ; Miltzow, Tillmann

The Complexity of the Hausdorff Distance

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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 ∀∃_<ℝ. This implies that the problem is NP-, co-NP-, ∃ℝ- and ∀ℝ-hard.

BibTeX - Entry

@InProceedings{jungeblut_et_al:LIPIcs.SoCG.2022.48,
  author =	{Jungeblut, Paul and Kleist, Linda and Miltzow, Tillmann},
  title =	{{The Complexity of the Hausdorff Distance}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{48:1--48:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16056},
  URN =		{urn:nbn:de:0030-drops-160567},
  doi =		{10.4230/LIPIcs.SoCG.2022.48},
  annote =	{Keywords: Hausdorff Distance, Semi-Algebraic Set, Existential Theory of the Reals, Universal Existential Theory of the Reals, Complexity Theory}
}

Keywords: Hausdorff Distance, Semi-Algebraic Set, Existential Theory of the Reals, Universal Existential Theory of the Reals, Complexity Theory
Collection: 38th International Symposium on Computational Geometry (SoCG 2022)
Issue Date: 2022
Date of publication: 01.06.2022

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