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Dynamic point location in general subdivisions

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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MPI-I-92-126.pdf
(Any fulltext), 9MB

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Citation

Baumgarten, H., Jung, H., & Mehlhorn, K.(1992). Dynamic point location in general subdivisions (MPI-I-92-126). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-B703-4
Abstract
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.