An algorithm for deciding if a polyomino tiles the plane
I Gambini, L Vuillon - RAIRO-Theoretical Informatics and Applications, 2007 - cambridge.org
I Gambini, L Vuillon
RAIRO-Theoretical Informatics and Applications, 2007•cambridge.org… One of his concerns was the design of a fast algorithm for computing the number of
polyominoes that tile the plane by translations. What he really had in mind was probably
their enumeration according to some convenient parameter. The algorithmic approach, by
providing computational evidence, is a convenient way to get some insight about the
algebricity or rationality of certain classes of … Nevertheless, from the algorithmic point of
view Nivat and Beauquier found a characterization of polyominoes that tile the plane by …
polyominoes that tile the plane by translations. What he really had in mind was probably
their enumeration according to some convenient parameter. The algorithmic approach, by
providing computational evidence, is a convenient way to get some insight about the
algebricity or rationality of certain classes of … Nevertheless, from the algorithmic point of
view Nivat and Beauquier found a characterization of polyominoes that tile the plane by …
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.
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