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

  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},
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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Publications referenced by this paper.
Showing 1-10 of 16 references

Stciger , and M . Szemerldi , An upper bound on the number of planar fc - sets

  • W. Pact
  • Combinatorial Geometry
  • 1995

Dissection graphs of plan : ur point sets

  • L. Lov P. Erdos
  • Allowable Sequences and Order Types in Discrete…
  • 1994

Fiiredi , and L . Lovdsz , On the number of halving planes , Combinatorica 10 ( 1990 ) , 175 - 183 . [ 4 ] L B 6 i & ay and W . Steiger , On the expected number of A - sets ,

  • H. Edelsbnmner B. Chazelle, L. Guibas, R. Seidel
  • Discrete Comput . Geom .
  • 1994

On the expected number of A-sets

  • L B6i, ay, W. Steiger
  • Discrete Comput. Geom
  • 1994
1 Excerpt

Clarkson , A bound on local minima of arrangements that implies the Upper Bound Theorem

  • Clarkson, P. Shor
  • Discrete Com - put . Geom .
  • 1993

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