Counting circular arc intersections

Pankaj K. Agarwal, Marco Pellegrini, Micha Sharir

Research output: Contribution to journalArticlepeer-review


In this paper efficient algorithms for counting intersections in a collection of circles or circular arcs are presented. An algorithm for counting intersections in a collection of n circles is presented whose running time is O(n3/2+ε), for any ε>0 is presented. Using this algorithm as a subroutine, it is shown that the intersections in a set of n circular arcs can also be counted in time O(n3/2+ε). If all arcs have the same radius, the running time can be improved to O(n4/3+ε), for any ε>0.

Original languageEnglish
Pages (from-to)778-793
Number of pages16
JournalSIAM Journal on Computing
Issue number4
StatePublished - 1993
Externally publishedYes


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