On Levels in Arrangements of Curves, II: A Simple Inequality and Its Consequences

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