Counting circular arc intersections

Pankaj K. Agarwal; Marco Pellegrini; Micha Sharir

doi:10.1137/0222050

Counting circular arc intersections

Pankaj K. Agarwal, Marco Pellegrini, Micha Sharir

Research output: Contribution to journal › Article › peer-review

Abstract

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(n^3/2+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(n^3/2+ε). If all arcs have the same radius, the running time can be improved to O(n^4/3+ε), for any ε>0.

Original language	English
Pages (from-to)	778-793
Number of pages	16
Journal	SIAM Journal on Computing
Volume	22
Issue number	4
DOIs	https://doi.org/10.1137/0222050
State	Published - 1993
Externally published	Yes

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abstract = "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.",

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year = "1993",

doi = "10.1137/0222050",

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Counting circular arc intersections

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