Dynamic Point Location in General Subdivisions
Kurt Mehlhorn (joint work with Hanna Baumgarten, Hermann Jung)
Max-Planck Institut für Informatik
email: mehlhorn@mpi-sb.mpg.de
Report B 92-10
March 92
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File: pub/reports/tr-b-92-10.ps.gz
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 \instime\ and deletion time \deltime. A query time
below \deltime\ was previously only known for monotone subdivisions and horizontal segments and required non-linear space.