An algorithm for deciding if a polyomino tiles the plane

Gambini, Ian; Vuillon, Laurent

doi:10.1051/ita:2007012

Geodesic

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An algorithm for deciding if a polyomino tiles the plane

Gambini, Ian ; Vuillon, Laurent

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 2, pp. 147-155.

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Résumé

For polyominoes coded by their boundary word, we describe a quadratic $O (n^{2})$ algorithm in the boundary length $n$ which improves the naive $O (n^{4})$ algorithm. Techniques used emanate from algorithmics, discrete geometry and combinatorics on words.

DOI : 10.1051/ita:2007012

Classification : 68R15, 52C20
Mots-clés : polyominoes, tiling the plane by translation, theorem of Beauquier-Nivat, pseudo-square, pseudo-hexagon, enumeration of special classes of polyominoes

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     author = {Gambini, Ian and Vuillon, Laurent},
     title = {An algorithm for deciding if a polyomino tiles the plane},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {147--155},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {2},
     year = {2007},
     doi = {10.1051/ita:2007012},
     mrnumber = {2350641},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2007012/}
}

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Gambini, Ian; Vuillon, Laurent. An algorithm for deciding if a polyomino tiles the plane. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 2, pp. 147-155. doi : 10.1051/ita:2007012. https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2007012/

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