MPI-I-92-126
Dynamic point location in general subdivisions
Baumgarten, Hanna and Jung, Hermann and Mehlhorn, Kurt
April 1992, 30 pages.
.
Status: available - back from printing
The {\em dynamic planar point location problem} is the
task of maintaining a dynamic set $S$ of $n$ non-intersecting, except
possibly at endpoints, line segments in the plane
under the following operations:
\begin{itemize}
\item Locate($q$: point): Report the
segment immediately above $q$, i.e., the first segment
intersected by an upward vertical ray starting at
$q$;
\item Insert($s$: segment): Add segment $s$ to the collection
$S$ of segments;
\item Delete($s$: segment): Remove segment $s$ from the
collection $S$ of segments.
\end{itemize}
We present a solution which requires space $O(n)$,
has query and insertion time and deletion time. A query time
was previously only known for monotone subdivisions and horizontal segments and required non-linear space.
URL to this document: https://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1992-126
BibTeX
@TECHREPORT{BaumgartenJungMehlhorn92,
AUTHOR = {Baumgarten, Hanna and Jung, Hermann and Mehlhorn, Kurt},
TITLE = {Dynamic point location in general subdivisions},
TYPE = {Research Report},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
NUMBER = {MPI-I-92-126},
MONTH = {April},
YEAR = {1992},
ISSN = {0946-011X},
}