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On Vertical Ray Shooting in Arrangements

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Jiri Matousek
Department of Computer Science
Charles University, CSFR
Report B 92-06
February 1992

Get the report here or by anonymous ftp:
Server: fubinf.inf.fu-berlin.de
File: pub/reports/tr-b-92-06.ps.gz

We consider the following problem: Given
a collection $H$ of $n$ hyperplanes in $\Ed$, preprocess it
so that given a query point $x$, a hyperplane of $H$
lying immediately above $x$ can be detected quickly. We give
a relatively simple solution with $O(n^d/\log^{d-1} n)$
space and deterministic preprocessing time and $O(\log n)$ query time.
This gives a slightly more efficient and considerably simplified
alternative of a previous solution due to Chazelle and Friedman.