On Levels in Arrangements of Lines, Segments, Planes, and Triangles%

@article{Agarwal1998OnLI,
  title={On Levels in Arrangements of Lines, Segments, Planes, and Triangles%},
  author={Pankaj K. Agarwal and Boris Aronov and Timothy M. Chan and Micha Sharir},
  journal={Discrete & Computational Geometry},
  year={1998},
  volume={19},
  pages={315-331}
}
We consider the problem of bounding the complexity of the fe-th level in an arran^ment of n curvra or surfM«s, a problem dual to, and «rtending, the iirell-known k-aet pmblem. (a) We review and simplify some old proofe in new disguise and give new proofis of the bonnd 0(n%/k +1) for the complexity of the fc-th level in an arran^ment of n lines, (b) We derive an improved version of LovAsz Lcnuna in any dimension, aad use it to prove a new bound, 0(n*it'^*), on the complexily of the ft-th level… CONTINUE READING
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