Rectangular tileability and complementary tileability are undecidable
Combinatorics
2012-12-17 v1 Computational Complexity
Computational Geometry
Abstract
Does a given a set of polyominoes tile some rectangle? We show that this problem is undecidable. In a different direction, we also consider tiling a cofinite subset of the plane. The tileability is undecidable for many variants of this problem. However, we present an algorithm for testing whether the complement of a finite region is tileable by a set of rectangles.
Cite
@article{arxiv.1212.3380,
title = {Rectangular tileability and complementary tileability are undecidable},
author = {Jed Yang},
journal= {arXiv preprint arXiv:1212.3380},
year = {2012}
}
Comments
16 pages, 8 figures