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 Dürr 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.
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© 2009 Springer-Verlag Berlin Heidelberg
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Dürr, C., Guiñez, F., Matamala, M. (2009). Reconstructing 3-Colored Grids from Horizontal and Vertical Projections Is NP-hard. In: Fiat, A., Sanders, P. (eds) Algorithms - ESA 2009. ESA 2009. Lecture Notes in Computer Science, vol 5757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04128-0_69
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DOI: https://doi.org/10.1007/978-3-642-04128-0_69
Publisher Name: Springer, Berlin, Heidelberg
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