MPI-INF/SWS Research Reports 1991-2021

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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.

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  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},