2026-07-24T08:01:26Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16024 2024-03-06T10:56:46Z ddc:004 open_access

Acute Tours in the Plane Biniaz, Ahmad planar points acute tour Hamiltonian cycle equitable partition We confirm the following conjecture of Fekete and Woeginger from 1997: for any sufficiently large even number n, every set of n points in the plane can be connected by a spanning tour (Hamiltonian cycle) consisting of straight-line edges such that the angle between any two consecutive edges is at most π/2. Our proof is constructive and suggests a simple O(nlog n)-time algorithm for finding such a tour. The previous best-known upper bound on the angle is 2π/3, and it is due to Dumitrescu, Pach and Tóth (2009). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ahmad Biniaz 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.2022.16 urn:nbn:de:0030-drops-160240 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.16 eng https://creativecommons.org/licenses/by/4.0/legalcode