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DOI: 10.4230/LIPIcs.ISAAC.2021.10
URN: urn:nbn:de:0030-drops-154431
URL: https://drops.dagstuhl.de/opus/volltexte/2021/15443/
Schnider, Patrick
Enclosing Depth and Other Depth Measures
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Abstract
We study families of depth measures defined by natural sets of axioms. We show that any such depth measure is a constant factor approximation of Tukey depth. We further investigate the dimensions of depth regions, showing that the Cascade conjecture, introduced by Kalai for Tverberg depth, holds for all depth measures which satisfy our most restrictive set of axioms, which includes Tukey depth. Along the way, we introduce and study a new depth measure called enclosing depth, which we believe to be of independent interest, and show its relation to a constant-fraction Radon theorem on certain two-colored point sets.
BibTeX - Entry
@InProceedings{schnider:LIPIcs.ISAAC.2021.10,
author = {Schnider, Patrick},
title = {{Enclosing Depth and Other Depth Measures}},
booktitle = {32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
pages = {10:1--10:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-214-3},
ISSN = {1868-8969},
year = {2021},
volume = {212},
editor = {Ahn, Hee-Kap and Sadakane, Kunihiko},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/15443},
URN = {urn:nbn:de:0030-drops-154431},
doi = {10.4230/LIPIcs.ISAAC.2021.10},
annote = {Keywords: Depth measures, Tukey depth, Tverberg theorem, Combinatorial Geometry}
}
| Keywords: | Depth measures, Tukey depth, Tverberg theorem, Combinatorial Geometry | |
| Seminar: | 32nd International Symposium on Algorithms and Computation (ISAAC 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 30.11.2021 |
