Reconstructing 3-colored grids from horizontal and vertical projections is NP-hard
| dc.creator | Durr, Christoph | |
| dc.creator | Guinez, Flavio | |
| dc.creator | Matamala, Martin | |
| dc.date | 2009-04-21 | |
| dc.date.accessioned | 2026-07-07T13:06:47Z | |
| dc.date.available | 2026-07-07T13:06:47Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0904.3169 | |
| dc.identifier | http://arxiv.org/abs/0904.3169 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227892 | |
| dc.subject | Data Structures and Algorithms | |
| dc.subject | Computational Complexity | |
| dc.title | Reconstructing 3-colored grids from horizontal and vertical projections is NP-hard | |
| dc.type | text |