Abstract
We fix two rectangles with integer dimensions. We give a quadratic time algorithm which, given a polygon F as input, produces a tiling of F with translated copies of our rectangles (or indicates that there is no tiling). Moreover, we prove that any pair of tilings can be linked by a sequence of local transformations of tilings, called flips. This study is based on the use of J. H. Conway’s tiling groups and extends the results of C. Kenyon and R. Kenyon (limited to the case when each rectangle has a side of length 1).
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Rémila, E. (2004). Tiling a Polygon with Two Kinds of Rectangles. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_51
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DOI: https://doi.org/10.1007/978-3-540-30140-0_51
Publisher Name: Springer, Berlin, Heidelberg
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