منابع مشابه
Coloring Points with Respect to Squares
We consider the problem of 2-coloring geometric hypergraphs. Specifically, we show that there is a constant m such that any finite set S of points in the plane can be 2-colored such that every axis-parallel square that contains at least m points from S contains points of both colors. Our proof is constructive, that is, it provides a polynomial-time algorithm for obtaining such a 2-coloring. By ...
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In a coloring of a set of points P with respect to a family of geometric regions one requires that in every region containing at least two points from P , not all the points are of the same color. Perhaps the most notorious open case is coloring of n points in the plane with respect to axis-parallel rectangles, for which it is known that O(n) colors always suffice, and Ω(log n/ log log n) color...
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متن کاملConflict-Free Coloring of Points on a Line with respect to a Set of Intervals
We present a 2-approximation algorithm for CFcoloring of points on a line with respect to a given set of intervals. The running time of the algorithm is O(n log n).
متن کاملFully-Dynamic and Kinetic Conflict-Free Coloring of Intervals with Respect to Points
We introduce the dynamic conflict-free coloring problem for a set S of intervals in R with respect to points, where the goal is to maintain a conflict-free coloring for S under insertions and deletions. We investigate trade-offs between the number of colors used and the number of intervals that are recolored upon insertion or deletion of an interval. Our results include: • a lower bound on the ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2017
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-017-9902-y