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Author Chan, Timothy M.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2001
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Computational geometry ♦ Convex hulls ♦ Dynamic data structures
Abstract We give a data structure that allows arbitrary insertions and deletions on a planar point set $\textit{P}$ and supports basic queries on the convex hull of $\textit{P},$ such as membership and tangent-finding. Updates take $\textit{O}(log1+ε\textit{n})$ amori tzed time and queries take $\textit{O}$ (log $\textit{n}$ time each, where $\textit{n}$ is the maximum size of $\textit{P}$ and ε is any fixed positive constant. For some advanced queries such as bridge-finding, both our bounds increase to $\textit{O}(log3/2\textit{n}).$ The only previous fully dynamic solution was by Overmars and van Leeuwen from 1981 and required $\textit{O}(log2\textit{n})$ time per update and $\textit{O}(log$ $\textit{n})$ time per query.
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 2001-01-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 48
Issue Number 1
Page Count 12
Starting Page 1
Ending Page 12


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Source: ACM Digital Library