@inproceedings{62ebfdec71894257918346cf6be58447,
title = "On rich lenses in planar arrangements of circles and related problems",
abstract = "We show that the maximum number of pairwise non-overlapping k-rich lenses (lenses formed by at least k circles) in an arrangement of n circles in the plane is O(n3/2 log(n/k3)k−5/2 + n/k), and the sum of the degrees of the lenses of such a family (where the degree of a lens is the number of circles that form it) is O(n3/2 log(n/k3)k−3/2 + n). Two independent proofs of these bounds are given, each interesting in its own right (so we believe). We then show that these bounds lead to the known bound of Agarwal et al. (JACM 2004) and Marcus and Tardos (JCTA 2006) on the number of point-circle incidences in the plane. Extensions to families of more general algebraic curves and some other related problems are also considered.",
keywords = "Circles, Incidences, Lenses, Polynomial partitioning",
author = "Esther Ezra and Raz, \{Orit E.\} and Micha Sharir and Joshua Zahl",
note = "Publisher Copyright: {\textcopyright} Esther Ezra, Orit E. Raz, Micha Sharir, and Joshua Zahl; licensed under Creative Commons License CC-BY 4.0 37th International Symposium on Computational Geometry (SoCG 2021).; 37th International Symposium on Computational Geometry, SoCG 2021 ; Conference date: 07-06-2021 Through 11-06-2021",
year = "2021",
month = jun,
day = "1",
doi = "10.4230/LIPIcs.SoCG.2021.35",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
pages = "35:1--35:15",
editor = "Kevin Buchin and \{de Verdiere\}, \{Eric Colin\}",
booktitle = "37th International Symposium on Computational Geometry, SoCG 2021",
address = "ألمانيا",
}