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

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.

Polyomino-Based Digital Halftoning

In this work, we present a new method for generating a threshold structure. This kind of structure can be advantageously used in various halftoning algorithms such as clustered-dot or dispersed-dot dithering, error diffusion with threshold modulation, etc. The proposed method is based on rectifiable polyominoes -a non-periodic hierarchical structure, which tiles the Euclidean plane with no gaps...

Optimal Partial Tiling of Manhattan Polyominoes

Finding an efficient optimal partial tiling algorithm is still an open problem. We have worked on a special case, the tiling of Manhattan polyominoes with dominoes, for which we give an algorithm linear in the number of columns. Some techniques are borrowed from traditional graph optimisation problems. For our purpose, a polyomino is the (non necessarily connected) union of unit squares (for wh...

Polyomino Convolutions and Tiling Problems

We define a convolution operation on the set of polyominoes and use it to obtain a criterion for a given polyomino not to tile the plane (rotations and translations allowed). We apply the criterion to several families of polyominoes, and show that the criterion detects some cases that are not detectable by generalized coloring arguments.

Isohedral Polyomino Tiling of the Plane