Cutting Circles into Pseudo-segments and Improved Bounds for Incidences
نویسندگان
چکیده
We show that n arbitrary circles in the plane can be cut into O(n) arcs, for any ε > 0, such that any pair of arcs intersect at most once. This improves a recent result of Tamaki and Tokuyama [20]. We use this result to obtain improved upper bounds on the number of incidences between m points and n circles. An improved incidence bound is also obtained for graphs of polynomials of any constant maximum degree.
منابع مشابه
Cutting Circles into Pseudo-Segments and Improved Bounds for Incidences% and Complexity of Many Faces
We show that n arbitrary circles in the plane can be cut into O(n) arcs, for any ε > 0, such that any pair of arcs intersect at most once. This improves a recent result of Tamaki and Tokuyama [20]. We use this result to obtain improved upper bounds on the number of incidences between m points and n circles. An improved incidence bound is also obtained for graphs of polynomials of any constant m...
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