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

dc.creatorDurr, Christoph
dc.creatorGuinez, Flavio
dc.creatorMatamala, Martin
dc.date2009-04-21
dc.date.accessioned2026-07-07T13:06:47Z
dc.date.available2026-07-07T13:06:47Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/0904.3169
dc.identifierhttp://arxiv.org/abs/0904.3169
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227892
dc.subjectData Structures and Algorithms
dc.subjectComputational Complexity
dc.titleReconstructing 3-colored grids from horizontal and vertical projections is NP-hard
dc.typetext

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