Reconstructing 3-colored grids from horizontal and vertical projections is NP-hard
Data Structures and Algorithms
2009-04-22 v1 Computational Complexity
Abstract
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.
Keywords
Cite
@article{arxiv.0904.3169,
title = {Reconstructing 3-colored grids from horizontal and vertical projections is NP-hard},
author = {Christoph Durr and Flavio Guinez and Martin Matamala},
journal= {arXiv preprint arXiv:0904.3169},
year = {2009}
}