, Volume 26, Issue 4, pp 573-590
Date: 01 Jan 2001

Hard Tiling Problems with Simple Tiles

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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.

Received March 8, 2000, and in revised form May 14, 2001, and June 18, 2001. Online publication October 12, 2001.