2026-07-21T14:19:09Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16067 2024-03-06T10:56:52Z ddc:004 open_access

Chains, Koch Chains, and Point Sets with Many Triangulations Rutschmann, Daniel Wettstein, Manuel Planar Point Set Chain Koch Chain Triangulation Maximum Number of Triangulations Lower Bound 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Daniel Rutschmann and Manuel Wettstein 2022 Is Part Of LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2022.59 urn:nbn:de:0030-drops-160678 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.59 eng https://creativecommons.org/licenses/by/4.0/legalcode