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Author Rubin, Natan
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2015
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Computational geometry ♦ Delaunay triangulation ♦ Voronoi diagram ♦ Combinatorial complexity ♦ Discrete changes ♦ Geometric arrangements ♦ Kinetic data structures ♦ Moving points
Abstract Let $\textit{P}$ be a collection of $\textit{n}$ 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 $DT(\textit{P})$ of $\textit{P}$ 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.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2015-06-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 62
Issue Number 3
Page Count 85
Starting Page 1
Ending Page 85


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Source: ACM Digital Library