Hard and Easy Instances of L-Tromino Tilings
Abstract
We study tilings of regions in the square lattice with L-shaped trominoes. Deciding the existence of a tiling with L-trominoes for an arbitrary region in general is NP-complete, nonetheless, we identify restrictions to the problem where it either remains NP-complete or has a polynomial time algorithm. First, we characterize the possibility of when an Aztec rectangle and an Aztec diamond has an L-tromino tiling. Then, we study tilings of arbitrary regions where only rotations of L-trominoes are available. For this particular case we show that deciding the existence of a tiling remains NP-complete; yet, if a region does not contains certain so-called "forbidden polyominoes" as sub-regions, then there exists a polynomial time algorithm for deciding a tiling.
Keywords
Cite
@article{arxiv.1710.04640,
title = {Hard and Easy Instances of L-Tromino Tilings},
author = {Javier T. Akagi and Carlos F. Gaona and Fabricio Mendoza and Manjil P. Saikia and Marcos Villagra},
journal= {arXiv preprint arXiv:1710.04640},
year = {2020}
}
Comments
Full extended version of LNCS 11355:82-95 (WALCOM 2019)