On kinetic delaunay triangulations: A near quadratic bound for unit speed motions

Natan Rubin

doi:10.1109/FOCS.2013.62

On kinetic delaunay triangulations: A near quadratic bound for unit speed motions

Natan Rubin

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

5 Scopus citations

Abstract

Let P be a collection of n points in the plane, each moving along some straight line at unit speed. We obtain an almost tight upper bound of O(n ^2+ε), for any ε > 0, on the maximum number of discrete changes that the Delaunay triangulation DT(P) of P experiences during this motion. Our analysis is cast in a purely topological setting, where we only assume that (i) any four points can be co-circular at most three times, and (ii) no triple of points can be collinear more than twice; these assumptions hold for unit speed motions.

Original language	English
Title of host publication	Proceedings - 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013
Pages	519-528
Number of pages	10
DOIs	https://doi.org/10.1109/FOCS.2013.62
State	Published - 1 Dec 2013
Externally published	Yes
Event	2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013 - Berkeley, CA, United States Duration: 27 Oct 2013 → 29 Oct 2013

Conference

Conference	2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013
Country/Territory	United States
City	Berkeley, CA
Period	27/10/13 → 29/10/13

Keywords

Combinatorial complexity
Delaunay triangulation
Discrete changes
Moving points
Voronoi diagram

ASJC Scopus subject areas

General Computer Science

Access to Document

10.1109/FOCS.2013.62

Cite this

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title = "On kinetic delaunay triangulations: A near quadratic bound for unit speed motions",

abstract = "Let P be a collection of n points in the plane, each moving along some straight line at unit speed. We obtain an almost tight upper bound of O(n 2+ε), for any ε > 0, on the maximum number of discrete changes that the Delaunay triangulation DT(P) of P experiences during this motion. Our analysis is cast in a purely topological setting, where we only assume that (i) any four points can be co-circular at most three times, and (ii) no triple of points can be collinear more than twice; these assumptions hold for unit speed motions.",

keywords = "Combinatorial complexity, Delaunay triangulation, Discrete changes, Moving points, Voronoi diagram",

author = "Natan Rubin",

year = "2013",

month = dec,

day = "1",

doi = "10.1109/FOCS.2013.62",

language = "English",

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pages = "519--528",

booktitle = "Proceedings - 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013",

note = "2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013 ; Conference date: 27-10-2013 Through 29-10-2013",

}

Rubin, N 2013, On kinetic delaunay triangulations: A near quadratic bound for unit speed motions. in Proceedings - 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013., 6686188, pp. 519-528, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013, Berkeley, CA, United States, 27/10/13. https://doi.org/10.1109/FOCS.2013.62

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N2 - Let P be a collection of n points in the plane, each moving along some straight line at unit speed. We obtain an almost tight upper bound of O(n 2+ε), for any ε > 0, on the maximum number of discrete changes that the Delaunay triangulation DT(P) of P experiences during this motion. Our analysis is cast in a purely topological setting, where we only assume that (i) any four points can be co-circular at most three times, and (ii) no triple of points can be collinear more than twice; these assumptions hold for unit speed motions.

AB - Let P be a collection of n points in the plane, each moving along some straight line at unit speed. We obtain an almost tight upper bound of O(n 2+ε), for any ε > 0, on the maximum number of discrete changes that the Delaunay triangulation DT(P) of P experiences during this motion. Our analysis is cast in a purely topological setting, where we only assume that (i) any four points can be co-circular at most three times, and (ii) no triple of points can be collinear more than twice; these assumptions hold for unit speed motions.

KW - Combinatorial complexity

KW - Delaunay triangulation

KW - Discrete changes

KW - Moving points

KW - Voronoi diagram

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DO - 10.1109/FOCS.2013.62

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BT - Proceedings - 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013

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ER -

On kinetic delaunay triangulations: A near quadratic bound for unit speed motions

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Keywords

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