Highly Influential

@inproceedings{Chan2003OnLI, title={On Levels in Arrangements of Curves, II: A Simple Inequality and Its Consequences}, author={Timothy M. Chan}, booktitle={FOCS}, year={2003} }

- Published 2003 in FOCS
DOI:10.1109/SFCS.2003.1238227

We give a surprisingly short proof that in any planar arrangement of n curves where each pair intersects at most a fixed number (s) of times, the k-level has subquadratic (O(n 1 2s )) complexity. This answers one of the main open problems from the author’s previous paper [Discrete Comput. Geom., 29:375–393, 2003], which provided a weaker upper bound for a restricted class of curves only (graphs of degree-s polynomials). When combined with existing tools (cutting curves, sampling, etc.), the new… CONTINUE READING