Geometric range searching

@article{Matousek1994GeometricRS,
  title={Geometric range searching},
  author={Jir{\'i} Matousek},
  journal={ACM Comput. Surv.},
  year={1994},
  volume={26},
  pages={421-461}
}
  • J. Matousek
  • Published 21 September 1994
  • Computer Science, Mathematics
  • ACM Comput. Surv.
In geometric range searching, algorithmic problems of the following type are considered. Given an n-point set P in the plane, build a data structure so that, given a query triangle R, the number of points of P lying in R can be determined quickly. Similar questions can be asked for point sets in higher dimensions, with triangles replaced by simplices or by more complicated shapes. Algorithms of this type are of crucial importance in computational geometry, as they can be used as subroutines in… 

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