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

Ramos, E. A. (1999). On range reporting, ray shooting and $k$-level construction. In Proceedings of the 15th Annual Symposium on Computational Geometry (SCG-99) (pp. 390-399). New York, USA: ACM.

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Datensatz-Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-35EA-F Versions-Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-35EB-D
Genre: Konferenzbeitrag

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 Urheber:
Ramos, Edgar A.1, Autor           
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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Schlagwörter: -
 Zusammenfassung: 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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Sprache(n): eng - English
 Datum: 2010-03-021999
 Publikationsstatus: Erschienen
 Seiten: -
 Ort, Verlag, Ausgabe: New York, USA : ACM
 Inhaltsverzeichnis: -
 Art der Begutachtung: -
 Identifikatoren: eDoc: 518062
Anderer: Local-ID: C1256428004B93B8-98DA48F941C5B6ABC12568AE0060B27F-Ramos1999
 Art des Abschluß: -

Veranstaltung

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Titel: Untitled Event
Veranstaltungsort: Miami Beach, Florida
Start-/Enddatum: 1999

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Titel: Proceedings of the 15th Annual Symposium on Computational Geometry (SCG-99)
Genre der Quelle: Konferenzband
 Urheber:
Affiliations:
Ort, Verlag, Ausgabe: New York, USA : ACM
Seiten: - Band / Heft: - Artikelnummer: - Start- / Endseite: 390 - 399 Identifikator: -