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Author Koltun, Vladlen
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2004
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Arrangements ♦ Decompositions ♦ Point location ♦ Range searching ♦ Ray shooting ♦ Robot motion planning
Abstract We show that the complexity of the vertical decomposition of an arrangement of $\textit{n}$ fixed-degree algebraic surfaces or surface patches in four dimensions is $O(n^{4+ϵ}),$ for any ϵ > 0. This improves the best previously known upper bound for this problem by a near-linear factor, and settles a major problem in the theory of arrangements of surfaces, open since 1989. The new bound can be extended to higher dimensions, yielding the bound $O(n^{2d™4+ϵ}),$ for any ϵ > 0, on the complexity of vertical decompositions in dimensions $\textit{d}$ ≥ 4. We also describe the immediate algorithmic applications of these results, which include improved algorithms for point location, range searching, ray shooting, robot motion planning, and some geometric optimization problems.
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 2004-09-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 51
Issue Number 5
Page Count 32
Starting Page 699
Ending Page 730


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Source: ACM Digital Library