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Minimal bounding rectangles are a simple and efficient tool for approximating geometries,
particularly for accelerating spatial queries. If a spatial object fills a rectangular shape
to a certain extent, then the minimal bounding rectangle is a reasonable approximation.
Unfortunately some geo objects, such as streets or rivers, have a small area but large
bounding rectangles. In our approach we suggest an approximation with two bounding rectangles
instead of a single one. Since the corresponding shape provides a better approximation, we
get a greater average benefit. We developed an efficient algorithm that computes the two
rectangles with the theoretically smallest combined area that encloses a given geometry
in O(n·log n) steps.
The algorithm is presented in
Jörg Roth:
The Approximation of TwoDimensional Spatial Objects by Two Bounding Rectangles
Spatial Cognition & Computation: An Interdisciplinary Journal, Volume 11, Issue 2, 2011, ISSN 13875868, 129152
A runtime of O(n·log n)
steps for n geometry points may be a crucial point for geometries with large amounts of geometry points. In a second approach,
we introduce an approximation that requires O(n) steps but only produces approx. 11% more false
hits compared to the theoretical optimum. The approximation is presented in
Jörg Roth:
An O(n) approximation for the double bounding box problem
IADIS International Conference Informatics 2011, Rome (Italy), July 2022, 2011, 2734
You can find the slides of the talk in Rome
here.

