Reconstructing 3-colored grids from horizontal and vertical projections is NP-hard

Details Reconstructing 3-colored grids from horizontal and vertical projections is NP-hard Reconstructing 3-colored grids from horizontal and vertical projections is NP-hard

2009-04-21

arxiv.org/abs/0904.3169v1

Computer Science

Data Structures and Algorithms

Scientific paper

We consider the problem of coloring a grid using k colors with the restriction that in each row and each column has an specific number of cells of each color. In an already classical result, Ryser obtained a necessary and sufficient condition for the existence of such a coloring when two colors are considered. This characterization yields a linear time algorithm for constructing such a coloring when it exists. Gardner et al. showed that for k>=7 the problem is NP-hard. Afterward Chrobak and Durr improved this result, by proving that it remains NP-hard for k>=4. We solve the gap by showing that for 3 colors the problem is already NP-hard. Besides we also give some results on tiling tomography problems.

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