On regular vertices on the union of planar objects

Esther Ezra; Janos Pach; Micha Sharir

doi:10.1145/1247069.1247110

On regular vertices on the union of planar objects

Esther Ezra^*, Janos Pach, Micha Sharir

^*Corresponding author for this work

School of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Let C be a collection of n compact convex sets in the plane, such that the boundaries of any pair of sets in C intersect in at most s points, for some constant s. We show that the maximum number of regular vertices (intersection points of two boundaries that intersect twice) on the boundary of the union U of C is O^*(n^4/3), which improves earlier bounds due to Aronov et.al.The bound is nearly tight in the worst case.

Original language	English
Title of host publication	Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07
Pages	220-226
Number of pages	7
DOIs	https://doi.org/10.1145/1247069.1247110
State	Published - 2007
Event	23rd Annual Symposium on Computational Geometry, SCG'07 - Gyeongju, Korea, Republic of Duration: 6 Jun 2007 → 8 Jun 2007

Publication series

Name	Proceedings of the Annual Symposium on Computational Geometry

Conference

Conference	23rd Annual Symposium on Computational Geometry, SCG'07
Country/Territory	Korea, Republic of
City	Gyeongju
Period	6/06/07 → 8/06/07

Keywords

(1/r)-cuttings
Regular vertices
Union of geometric objects

Access to Document

10.1145/1247069.1247110

Cite this

@inproceedings{a9451fa4fe044e1983fa004d350cc8e0,

title = "On regular vertices on the union of planar objects",

abstract = "Let C be a collection of n compact convex sets in the plane, such that the boundaries of any pair of sets in C intersect in at most s points, for some constant s. We show that the maximum number of regular vertices (intersection points of two boundaries that intersect twice) on the boundary of the union U of C is O*(n4/3), which improves earlier bounds due to Aronov et.al.The bound is nearly tight in the worst case.",

keywords = "(1/r)-cuttings, Regular vertices, Union of geometric objects",

author = "Esther Ezra and Janos Pach and Micha Sharir",

year = "2007",

doi = "10.1145/1247069.1247110",

language = "אנגלית",

isbn = "1595937056",

series = "Proceedings of the Annual Symposium on Computational Geometry",

pages = "220--226",

booktitle = "Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07",

note = "23rd Annual Symposium on Computational Geometry, SCG'07 ; Conference date: 06-06-2007 Through 08-06-2007",

}

Ezra, E, Pach, J & Sharir, M 2007, On regular vertices on the union of planar objects. in Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07. Proceedings of the Annual Symposium on Computational Geometry, pp. 220-226, 23rd Annual Symposium on Computational Geometry, SCG'07, Gyeongju, Korea, Republic of, 6/06/07. https://doi.org/10.1145/1247069.1247110

TY - GEN

T1 - On regular vertices on the union of planar objects

AU - Ezra, Esther

AU - Pach, Janos

AU - Sharir, Micha

PY - 2007

Y1 - 2007

N2 - Let C be a collection of n compact convex sets in the plane, such that the boundaries of any pair of sets in C intersect in at most s points, for some constant s. We show that the maximum number of regular vertices (intersection points of two boundaries that intersect twice) on the boundary of the union U of C is O*(n4/3), which improves earlier bounds due to Aronov et.al.The bound is nearly tight in the worst case.

AB - Let C be a collection of n compact convex sets in the plane, such that the boundaries of any pair of sets in C intersect in at most s points, for some constant s. We show that the maximum number of regular vertices (intersection points of two boundaries that intersect twice) on the boundary of the union U of C is O*(n4/3), which improves earlier bounds due to Aronov et.al.The bound is nearly tight in the worst case.

KW - (1/r)-cuttings

KW - Regular vertices

KW - Union of geometric objects

UR - http://www.scopus.com/inward/record.url?scp=35348867384&partnerID=8YFLogxK

U2 - 10.1145/1247069.1247110

DO - 10.1145/1247069.1247110

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:35348867384

SN - 1595937056

SN - 9781595937056

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 220

EP - 226

BT - Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07

T2 - 23rd Annual Symposium on Computational Geometry, SCG'07

Y2 - 6 June 2007 through 8 June 2007

ER -

On regular vertices on the union of planar objects

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this