License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2016.50
URN: urn:nbn:de:0030-drops-59423
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5942/
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Langerman, Stefan ; Winslow, Andrew

A Quasilinear-Time Algorithm for Tiling the Plane Isohedrally with a Polyomino

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LIPIcs-SoCG-2016-50.pdf (0.6 MB)

Abstract

A plane tiling consisting of congruent copies of a shape is isohedral provided that for any pair of copies, there exists a symmetry of the tiling mapping one copy to the other. We give a O(n*log^2(n))-time algorithm for deciding if a polyomino with n edges can tile the plane isohedrally. This improves on the O(n^{18})-time algorithm of Keating and Vince and generalizes recent work by Brlek, Provençal, Fédou, and the second author.

BibTeX - Entry

@InProceedings{langerman_et_al:LIPIcs:2016:5942,
  author =	{Stefan Langerman and Andrew Winslow},
  title =	{{A Quasilinear-Time Algorithm for Tiling the Plane Isohedrally with a Polyomino}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{50:1--50:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{S{\'a}ndor Fekete and Anna Lubiw},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5942},
  URN =		{urn:nbn:de:0030-drops-59423},
  doi =		{10.4230/LIPIcs.SoCG.2016.50},
  annote =	{Keywords: Plane tiling, polyomino, boundary word, isohedral}
}

Keywords: Plane tiling, polyomino, boundary word, isohedral
Collection: 32nd International Symposium on Computational Geometry (SoCG 2016)
Issue Date: 2016
Date of publication: 10.06.2016

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