# Fast Domino Tileability

@article{Pak2016FastDT, title={Fast Domino Tileability}, author={Igor Pak and Adam Sheffer and Martin Tassy}, journal={Discrete \& Computational Geometry}, year={2016}, volume={56}, pages={377-394} }

Abstract Domino tileability is a classical problem in Discrete Geometry, famously solved by Thurston for simply connected regions in nearly linear time in the area. In this paper, we improve upon Thurston’s height function approach to a nearly linear time in the perimeter.

## 10 Citations

Tiling with Squares and Packing Dominos in Polynomial Time

- Computer ScienceSoCG
- 2022

The standard, compact way to represent a polygon is by listing the coordinates of the corners in binary, and thus the first polynomial time algorithms for the problems are presented, including a simple $O(n\log n) $ algorithm for tiling with squares, and a more involved $O (n^4)$ algorithm for packing and tiled with dominos.

MIXING PROPERTIES OF COLORINGS OF THE Z LATTICE

- Mathematics
- 2019

We study and classify proper q-colorings of the Zd lattice, identifying three regimes where different combinatorial behavior holds: (1) When q ≤ d + 1, there exist frozen colorings, that is, proper…

A quenched variational principle for discrete random maps

- Mathematics
- 2017

We study the variational principle for discrete height functions (or equivalently domino tilings) where the underlying measure is perturbed by a random field. We show that the variational principle…

Mixing properties of colourings of the ℤd lattice

- MathematicsComb. Probab. Comput.
- 2021

A strong list-colours property is proved which implies that, when $q\ge d+2$ , any proper q-colouring of the boundary of a box of side length $n \ge d-2$ can be extended to a properq-coloured of the entire box.

Mixing properties of colorings of the $\mathbb{Z}^d$ lattice

- Mathematics
- 2019

We study and classify proper $q$-colorings of the $\mathbb Z^d$ lattice, identifying three regimes where different combinatorial behavior holds: (1) When $q\le d+1$, there exist frozen colorings,…

Borel subsystems and ergodic universality for compact Zd ‐systems via specification and beyond

- MathematicsProceedings of the London Mathematical Society
- 2021

A Borel Zd dynamical system (X,S) is ‘almost Borel universal’ if any free Borel Zd dynamical system (Y,T) of strictly lower entropy is isomorphic to a Borel subsystem of (X,S) , after removing a null…

A variational principle for a non-integrable model

- MathematicsProbability Theory and Related Fields
- 2020

We show the existence of a variational principle for graph homomorphisms from $$\mathbb {Z}^m$$ Z m to a d -regular tree. The technique is based on a discrete Kirszbraun theorem and a concentration…

Asymptotics for the number of standard tableaux of skew shape and for weighted lozenge tilings

- MathematicsComb. Probab. Comput.
- 2022

<jats:p>We prove and generalise a conjecture in [MPP4] about the asymptotics of <jats:inline-formula>
<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink"…

Borel subsystems and ergodic universality for compact $\mathbb Z^d$-systems via specification and beyond

- Mathematics
- 2019

A Borel system $(X,S)$ is `almost Borel universal' if any free Borel dynamical system $(Y,T)$ of strictly lower entropy is isomorphic to a Borel subsystem of $(X,S)$, after removing a null set. We…

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