English

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.

Keywords

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

R2 v1 2026-06-21T22:54:21.773Z