License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2022.16
URN: urn:nbn:de:0030-drops-160240
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Biniaz, Ahmad

Acute Tours in the Plane

LIPIcs-SoCG-2022-16.pdf (0.7 MB)


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).

BibTeX - Entry

  author =	{Biniaz, Ahmad},
  title =	{{Acute Tours in the Plane}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{16:1--16:8},
  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 =		{},
  URN =		{urn:nbn:de:0030-drops-160240},
  doi =		{10.4230/LIPIcs.SoCG.2022.16},
  annote =	{Keywords: planar points, acute tour, Hamiltonian cycle, equitable partition}

Keywords: planar points, acute tour, Hamiltonian cycle, equitable partition
Collection: 38th International Symposium on Computational Geometry (SoCG 2022)
Issue Date: 2022
Date of publication: 01.06.2022

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