Cutting circles into pseudo-segments and improved bounds for incidences

Boris Aronov*, Micha Sharir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We show that n arbitrary circles in the plane can be cut into O(n3/2+ε) arcs, for any ε > 0, such that any pair of arcs intersects 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.

Original languageEnglish
Pages (from-to)475-490
Number of pages16
JournalDiscrete and Computational Geometry
Issue number4
StatePublished - Dec 2002


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