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On the tiling by translation problem

Srecko Brlek 1 Xavier Provençal 1 Jean-Marc Fédou 2
1 LaCIM - Laboratoire de combinatoire et d'informatique mathématique [Montréal]
2 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe MC3
Laboratoire I3S - MDSC - Modèles Discrets pour les Systèmes Complexes
Abstract : On square or hexagonal lattices, tiles or polyominoes are coded by words. The polyominoes that tile the plane by translation are characterized by the Beauquier-Nivat condition. By using the constant time algorithms for computing the longest common extensions in two words, we provide a linear time algorithm in the case of pseudo-square polyominoes, improving the previous quadratic algorithm of Gambini and Vuillon. We also have a linear algorithm for pseudo-hexagon polyominoes not containing arbitrarily large square factors. The results are extended to more general tiles.
Mots-clés : Tiling polyominoes Plane tesselation Longest common extensions
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https://hal.archives-ouvertes.fr/hal-00395229
Contributor : Xavier Provençal <>
Submitted on : Monday, June 15, 2009 - 11:49:09 AM
Last modification on : Wednesday, October 14, 2020 - 4:16:42 AM

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Srecko Brlek, Xavier Provençal, Jean-Marc Fédou. On the tiling by translation problem. Discrete Applied Mathematics, Elsevier, 2008, 157 (3), pp.464-475. ⟨10.1016/j.dam.2008.05.026⟩. ⟨hal-00395229⟩

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