Colorful Strips

We study the following geometric hypergraph coloring problem: given a planar point set and an integer k, we wish to color the points with k colors so that any axis-aligned strip containing sufficiently many points contains all colors. We show that if the strip contains at least 2k−1 points, such a coloring can always be found. In dimension d, we show that the same holds provided the strip contains at least k(4lnk +lnd) points. We also consider the dual problem of coloring a given set of axis-aligned strips so that any sufficiently covered point in the plane is covered by k colors. We show that in dimension d the required

• Type: Conference
• Year: 2010
• Where: LATIN
• Authors: Greg Aloupis, Jean Cardinal, Sébastien Collette, Shinji Imahori, Matias Korman, Stefan Langerman, Oded Schwartz, Shakhar Smorodinsky, Perouz Taslakian
• Keywords: Axis-aligned Strips, Hypergraph Coloring Problem, Information Retrieval, LATIN 2010, Planar Point