An algorithm for deciding if a polyomino tiles the plane

An algorithm for deciding if a polyomino tiles the plane

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

An algorithm for deciding if a polyomino tiles the plane by translations

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

On the problem of deciding if a polyomino tiles the plane by translation

An Optimal Algorithm for Tiling the Plane with a Translated Polyomino

We give aO(n)-time algorithm for determining whether translations of a polyomino with n edges can tile the plane. The algorithm is also a O(n)-time algorithm for enumerating all regular tilings, and we prove that at most Θ(n) such tilings exist.

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

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 log2 n)-time algorithm for deciding if a polyomino with n edges can tile the plane isohedrally. This improves on the O(n18)-time algorithm of Keating and Vince and generalizes recent work by Brlek, Provença...