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DOI: 10.4230/LIPIcs.SoCG.2022.48
URN: urn:nbn:de:0030-drops-160567
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16056/
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 | |
| Seminar: | 38th International Symposium on Computational Geometry (SoCG 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 01.06.2022 |
