On the tiling by translation problem
Discrete Applied Mathematics（2009）
摘要
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.
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关键词
general tile,longest common extensions,pseudo-square polyominoes,plane tesselation,previous quadratic algorithm,hexagonal lattice,constant time algorithm,beauquier-nivat condition,translation problem,large square factor,linear time algorithm,tiling polyominoes,pseudo-hexagon polyominoes,linear algorithm
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