Discrete & Computational Geometry

, Volume 26, Issue 4, pp 573–590

Hard Tiling Problems with Simple Tiles

  • C. Moore
  • J.M. Robson

DOI: 10.1007/s00454-001-0047-6

Cite this article as:
Moore, C. & Robson, J. Discrete Comput Geom (2001) 26: 573. doi:10.1007/s00454-001-0047-6


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.

Copyright information

© Springer-Verlag New York Inc. 2001

Authors and Affiliations

  • C. Moore
    • 1
  • J.M. Robson
  1. 1.Computer Science Department, University of New Mexico, Albuquerque, NM 87131, USAUSA