Some new bounds for Epsilon-nets
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Almost tight bounds for &egr;-nets
Discrete & Computational Geometry
Lectures on Discrete Geometry
WG '88 Proceedings of the 14th International Workshop on Graph-Theoretic Concepts in Computer Science
Restricted strip covering and the sensor cover problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Multiple Coverings of the Plane with Triangles
Discrete & Computational Geometry
Decomposition of multiple coverings into many parts
Computational Geometry: Theory and Applications
Coloring Geometric Range Spaces
Discrete & Computational Geometry
Convex Polygons are Cover-Decomposable
Discrete & Computational Geometry
Decomposing Coverings and the Planar Sensor Cover Problem
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
Indecomposable Coverings with Concave Polygons
Discrete & Computational Geometry
Decomposition of Multiple Coverings into More Parts
Discrete & Computational Geometry
Graphs and Combinatorics - The Japan Conference on Computational Geometry and Graphs (JCCGG2009)
Coloring hypergraphs induced by dynamic point sets and bottomless rectangles
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We prove that for every integer k, every finite set of points in the plane can be k-colored so that every half-plane that contains at least 2k-1 points, also contains at least one point from every color class. We also show that the bound 2k-1 is best possible. This improves the best previously known lower and upper bounds of 43k and 4k-1 respectively. We also show that every finite set of half-planes can be k-colored so that if a point p belongs to a subset H"p of at least 3k-2 of the half-planes then H"p contains a half-plane from every color class. This improves the best previously known upper bound of 8k-3. Another corollary of our first result is a new proof of the existence of small size @e-nets for points in the plane with respect to half-planes.