| Issue |
RAIRO-Theor. Inf. Appl.
Volume 41, Number 2, April-June 2007
|
|
|---|---|---|
| Page(s) | 147 - 155 | |
| DOI | https://doi.org/10.1051/ita:2007012 | |
| Published online | 18 July 2007 | |
An algorithm for deciding if a polyomino tiles the plane
1
Laboratoire d'Informatique Fondamentale de Marseille, CNRS UMR 6166, Université de la Méditerranée, 163 avenue de Luminy - Case 901, 13288 Marseille Cedex 9, France; Ian.Gambini@lif.univ-mrs.fr
2
Laboratoire de Mathématiques, CNRS UMR 5127, Université de Savoie, 73376, le Bourget-du-Lac, France; Laurent.Vuillon@univ-savoie.fr
Received:
11
February
2005
Accepted:
3
April
2006
For polyominoes coded by their boundary word, we describe a quadratic O(n2) algorithm in the boundary length n which improves the naive O(n4) algorithm. Techniques used emanate from algorithmics, discrete geometry and combinatorics on words.
Mathematics Subject Classification: 68R15 / 52C20
Key words: Polyominoes / tiling the plane by translation / theorem of Beauquier-Nivat / pseudo-square / pseudo-hexagon / enumeration of special classes of polyominoes
© EDP Sciences, 2007
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