Hard Tiling Problems with Simple Tiles

Cristopher Moore and John Michael Robson

Working Papers from Santa Fe Institute

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.

Keywords: Tilings; dominoes; polyominoes. (search for similar items in EconPapers)
Date: 2000-03
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Persistent link: https://EconPapers.repec.org/RePEc:wop:safiwp:00-03-019

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