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arXiv · 1507.02762

A Quasilinear-Time Algorithm for Tiling the Plane Isohedrally with a Polyomino

Stefan Langerman·Andrew Winslow
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Abstract

A plane tiling consisting of congruent copies of a shape is isohedral provided that for any pair of copies, there exists a symmetry of the tiling mapping one copy to the other. We give a $O(n\log^2{n})$-time algorithm for deciding if a polyomino with $n$ edges can tile the plane isohedrally. This improves on the $O(n^{18})$-time algorithm of Keating and Vince and generalizes recent work by Brlek, Proven\c{c}al, F\'{e}dou, and the second author.

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Stefan Langerman, Andrew Winslow. 2015-07-10. A Quasilinear-Time Algorithm for Tiling the Plane Isohedrally with a Polyomino. https://arxiv.org/abs/1507.02762

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