When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2022.9
URN: urn:nbn:de:0030-drops-160170
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16017/
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### Tighter Bounds for Reconstruction from ε-Samples

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### Abstract

We show that reconstructing a curve in ℝ^d for d ≥ 2 from a 0.66-sample is always possible using an algorithm similar to the classical NN-Crust algorithm. Previously, this was only known to be possible for 0.47-samples in ℝ² and 1/3-samples in ℝ^d for d ≥ 3. In addition, we show that there is not always a unique way to reconstruct a curve from a 0.72-sample; this was previously only known for 1-samples. We also extend this non-uniqueness result to hypersurfaces in all higher dimensions.

### BibTeX - Entry

@InProceedings{bakkebjerkevik:LIPIcs.SoCG.2022.9,
author =	{Bakke Bjerkevik, H\r{a}vard},
title =	{{Tighter Bounds for Reconstruction from \epsilon-Samples}},
booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
pages =	{9:1--9:17},
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},
}