Hard Tiling Problems with Simple Tiles
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- Moore, C. & Robson, J. Discrete Comput Geom (2001) 26: 573. doi:10.1007/s00454-001-0047-6
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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.