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DOI: 10.4230/LIPIcs.SoCG.2022.59
URN: urn:nbn:de:0030-drops-160678
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16067/
Rutschmann, Daniel ; Wettstein, Manuel
Chains, Koch Chains, and Point Sets with Many Triangulations
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Abstract
We introduce the abstract notion of a chain, which is a sequence of n points in the plane, ordered by x-coordinates, so that the edge between any two consecutive points is unavoidable as far as triangulations are concerned. A general theory of the structural properties of chains is developed, alongside a general understanding of their number of triangulations.We also describe an intriguing new and concrete configuration, which we call the Koch chain due to its similarities to the Koch curve. A specific construction based on Koch chains is then shown to have Ω(9.08ⁿ) triangulations. This is a significant improvement over the previous and long-standing lower bound of Ω(8.65ⁿ) for the maximum number of triangulations of planar point sets.
BibTeX - Entry
@InProceedings{rutschmann_et_al:LIPIcs.SoCG.2022.59,
author = {Rutschmann, Daniel and Wettstein, Manuel},
title = {{Chains, Koch Chains, and Point Sets with Many Triangulations}},
booktitle = {38th International Symposium on Computational Geometry (SoCG 2022)},
pages = {59:1--59:18},
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/2022/16067},
URN = {urn:nbn:de:0030-drops-160678},
doi = {10.4230/LIPIcs.SoCG.2022.59},
annote = {Keywords: Planar Point Set, Chain, Koch Chain, Triangulation, Maximum Number of Triangulations, Lower Bound}
}
| Keywords: | Planar Point Set, Chain, Koch Chain, Triangulation, Maximum Number of Triangulations, Lower Bound | |
| Seminar: | 38th International Symposium on Computational Geometry (SoCG 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 01.06.2022 |
