Hard Tiling Problems with Simple Tiles
نویسندگان
چکیده
منابع مشابه
Hard Tiling Problems with Simple Tiles
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 ...
متن کاملTiling with Small Tiles
We look at sets of tiles that can tile any region of size greater than 1 on the square grid. This is not the typical tiling question, but relates closely to it and therefore can help solve other tiling problems – we give an example of this. We also present a result to a more classic tiling question with dominoes and L-shape tiles.
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A finite subset A of integers tiles the discrete line Z if the integers can be written as a disjoint union of translates of A. In some cases, necessary and sufficient conditions for A to tile the integers are known. We extend this result to a large class of nonperiodic tilings and give a new formulation of the Coven-Meyerowitz reciprocity conjecture which is equivalent to the Flugede conjecture...
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The undecidable problems we saw at the start of our unit on undecidability were all questions about the behavior of computer programs. But in fact there are many decision problems which, on the surface, have nothing to do with computer programs yet can still be proved to have no algorithmic solution. One of these is a tiling problem. Imagine square tiles divided into colored triangular quadrants.
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We study the computational complexity of a variant of the popular 2048 game in which no new tiles are generated after each move. As usual, instances are defined on rectangular boards of arbitrary size. We consider the natural decision problems of achieving a given constant tile value, score or number of moves. We also consider approximating the maximum achievable value for these three objective...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2001
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-001-0047-6