par Cardinal, Jean 
;Cohen, Nathann ;Collette, Sébastien ;Hoffmann, Michael;Langerman, Stefan ;Rote, Günter
Référence European Workshop on Computational Geometry(XXVIII: 19-21 March, 2012: Assisi, Italy), Proceedings of the EuroCG 2012, page (209-211)
Publication Publié, 2012-03
;Cohen, Nathann ;Collette, Sébastien ;Hoffmann, Michael;Langerman, Stefan ;Rote, GünterRéférence European Workshop on Computational Geometry(XXVIII: 19-21 March, 2012: Assisi, Italy), Proceedings of the EuroCG 2012, page (209-211)
Publication Publié, 2012-03
Publication dans des actes
| Résumé : | We consider a coloring problem on dynamic, one-dimensional point sets: points appearing and disappearing on a line at given times. We wish to color them with k colors so that at any time, any sequence of p(k) consecutive points, for some function p, contains at least one point of each color.We prove that no such function p(k) exists in general. However, in the restricted case in which points appear gradually, but never disappear, we give a coloring algorithm guaranteeing the property at any time with p(k)=8k-4. This can be interpreted as coloring point sets in R^2 with k colors such that any bottomless rectangle containing at least 8k-5 points contains at least one point of each color. Chen et al. (2009) proved that such colorings do not always exist in the case of general axis-aligned rectangles. Our result also complements recent results from Keszegh and Pálvölgyi (2011). |
