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Hard Tiling Problems with Simple Tiles

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  • Cristopher Moore
  • John Michael Robson
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    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.

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    Bibliographic Info

    Paper provided by Santa Fe Institute in its series Working Papers with number 00-03-019.

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    Date of creation: Mar 2000
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    Handle: RePEc:wop:safiwp:00-03-019

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    Related research

    Keywords: Tilings; dominoes; polyominoes.;

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