Range searching with efficient hierarchical cuttings

@article{Matouek1992RangeSW,
  title={Range searching with efficient hierarchical cuttings},
  author={Jiř{\'i} Matou{\vs}ek},
  journal={Discrete \& Computational Geometry},
  year={1992},
  volume={10},
  pages={157-182}
}
  • J. Matoušek
  • Published 1 July 1992
  • Computer Science
  • Discrete & Computational Geometry
AbstractWe present an improved space/query-time tradeoff for the general simplex range searching problem, matching known lower bounds up to small polylogarithmic factors. In particular, we construct a linear-space simplex range searching data structure withO(n1−1/d) query time, which is optimal ford=2 and probably also ford>2. Further, we show that multilevel range searching data structures can be built with only a polylogarithmic overhead in space and query time per level (the previous… 
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