Hard Tiling Problems with Simple Tiles
AbstractIt 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 tthat 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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Bibliographic InfoPaper provided by Santa Fe Institute in its series Working Papers with number 00-03-019.
Date of creation: Mar 2000
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Tilings; dominoes; polyominoes.;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2000-04-26 (All new papers)
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