Discrete and Computational Geometry 26(4) (2001) 573--590.
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.
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