On Kinetic Delaunay Triangulations
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Published:2015-06-30
Issue:3
Volume:62
Page:1-85
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ISSN:0004-5411
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Container-title:Journal of the ACM
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language:en
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Short-container-title:J. ACM
Affiliation:
1. Ben-Gurion University of The Negev, Israel
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.
Funder
Fondation Sciences Mathématiques de Paris
Minerva Fellowship Program of the Max Planck Society
public grant overseen by the French National Research Agency (ANR) as part of the Investissements d'Avenir program
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
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