2026-07-25T09:16:51Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23207 2025-10-27T07:47:25Z ddc:004 open_access

A Practical Algorithm for Knot Factorisation He, Alexander Sedgwick, Eric Spreer, Jonathan Prime and composite knots (crushing) normal surfaces edge-ideal triangulations co-NP certificate triangulation complexity We present an algorithm for computing the prime factorisation of a knot, which is practical in the following sense: using Regina, we give an implementation that works well for inputs of reasonable size, including prime knots from the 19-crossing census. The main new ingredient in this work is an object that we call an "edge-ideal triangulation", which is what our algorithm uses to represent knots. As other applications, we give an alternative proof that prime knot recognition is in coNP, and present some new complexity results for triangulations. Beyond knots, our work showcases edge-ideal triangulations as a tool for potential applications in 3-manifold topology. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Alexander He and Eric Sedgwick and Jonathan Spreer 2025 Is Part Of LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2025.55 urn:nbn:de:0030-drops-232075 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.55 eng https://creativecommons.org/licenses/by/4.0/legalcode