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- W2110107802 abstract "We consider the problem of coloring a grid using $k$ colors with the restriction that each row and each column has a specific number of cells of each color. This problem has been known as the $(k-1)$-atom problem in the discrete tomography community. 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 $kgeqslant 7$ the problem is NP-hard. Afterward Chrobak and Durr improved this result by proving that it remains NP-hard for $kgeqslant 4$. We close the gap by showing that for $k=3$ colors the problem is already NP-hard. In addition, we give some results on tiling tomography problems." @default.
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- W2110107802 date "2012-01-01" @default.
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- W2110107802 title "Reconstructing 3-Colored Grids from Horizontal and Vertical Projections is NP-Hard: A Solution to the 2-Atom Problem in Discrete Tomography" @default.
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- W2110107802 doi "https://doi.org/10.1137/100799733" @default.
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