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Hard Tiling Problems with Simple Tiles

Author

Listed:
  • Cristopher Moore
  • John Michael Robson

Abstract

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 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.

Suggested Citation

  • Cristopher Moore & John Michael Robson, 2000. "Hard Tiling Problems with Simple Tiles," Working Papers 00-03-019, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:00-03-019
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    Keywords

    Tilings; dominoes; polyominoes.;
    All these keywords.

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