Hard Tiling Problems with Simple Tiles
Combinatorics
2007-05-23 v1
Abstract
It is well-known that the question of whether a given finite region can be tiled with a given set of tiles is NP-complete. We show that the same is true for the right tromino and square tetromino on the square lattice, or for the right tromino alone. In the process, we show that Monotone 1-in-3 Satisfiability is NP-complete for planar cubic graphs. In higher dimensions, we show NP-completeness for the domino and straight tromino for general regions on the cubic lattice, and for simply-connected regions on the four-dimensional hypercubic lattice.
Keywords
Cite
@article{arxiv.math/0003039,
title = {Hard Tiling Problems with Simple Tiles},
author = {Cristopher Moore and John Michael Robson},
journal= {arXiv preprint arXiv:math/0003039},
year = {2007}
}