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Author, Editor

Author(s):

Ramos, Edgar A.

dblp



Editor(s):





BibTeX cite key*:

Ramos1999

Title, Booktitle

Title*:

On range reporting, ray shooting and $k$-level construction

Booktitle*:

Proceedings of the 15th Annual Symposium on Computational Geometry (SCG-99)

Event, URLs

URL of the conference:


URL for downloading the paper:


Event Address*:

Miami Beach, Florida

Language:

English

Event Date*
(no longer used):

June 13-16, 1999

Organization:


Event Start Date:

19 September 2019

Event End Date:

19 September 2019

Publisher

Name*:

ACM

URL:


Address*:

New York, USA

Type:


Vol, No, Year, pp.

Series:


Volume:


Number:


Month:


Pages:

390-399

Year*:

1999

VG Wort Pages:


ISBN/ISSN:


Sequence Number:


DOI:




Note, Abstract, ©


(LaTeX) Abstract:

We describe the following data structures. For halfspace range reporting,
in 3-space using expected preprocessing time $O(n\log n)$, worst case storage
$O(n\log\log n)$ and worst case reporting time $O(\log n+k)$ where $n$ is
the number of data points and $k$ the number of points reported; in $d$-space,
with $d$ even, using worst case preprocessing time $O(n\log n)$ and storage
$O(n)$ and reporting time $O(n^{1-1/\lfloor d/2\rfloor}\log^c n+k)$. For ray
shooting in a convex polytope determined by $n$ facets using deterministic
preprocessing time $O((n/\log n)^{\floor{d/2}}\log^c n)$ and storage $O((n/
\log n)^{\lfloor d/2 \rfloor}2^{\log^* n})$ and with query time $O(\log n)$.
For ray shooting in arbitrary direction among $n$ hyperplanes using preprocessing
$O(n^d/ \log^{\floor{d/2}} n)$ and query time $O(\log n)$. We also
describe algorithms to construct the $k$-level of $n$ planes in 3-space dual
to points in convex position: the first one is randomized and uses nearly optimal
expected time $O(n\log n + nk2^{c\log^* k})$ and the second one is deterministic
and uses time $O(nk\log^c n)$. By a standard geometric transformation the same
time bound applies for the construction of the $k$-order Voronoi diagram of $n$
sites in the plane.



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Correlation

MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Algorithms and Complexity Group

Audience:

experts only

Appearance:

MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat



BibTeX Entry:

@INPROCEEDINGS{Ramos1999,
AUTHOR = {Ramos, Edgar A.},
TITLE = {On range reporting, ray shooting and $k$-level construction},
BOOKTITLE = {Proceedings of the 15th Annual Symposium on Computational Geometry (SCG-99)},
PUBLISHER = {ACM},
YEAR = {1999},
PAGES = {390--399},
ADDRESS = {Miami Beach, Florida},
}


Entry last modified by Uwe Brahm, 03/02/2010
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Editor(s)
Edgar A. Ramos
Created
03/26/2000 07:36:11 PM
Revisions
3.
2.
1.
0.
Editor(s)
Uwe Brahm
Anja Becker
Anja Becker
Edgar A. Ramos
Edit Dates
04/04/2001 07:43:49 PM
30.03.2000 12:24:03
29.03.2000 16:28:29
26/03/2000 19:36:11