Tight lower bounds for halfspace range searching

@article{Arya2010TightLB,
  title={Tight lower bounds for halfspace range searching},
  author={Sunil Arya and David M. Mount and Jian Xia},
  journal={Discrete & Computational Geometry},
  year={2010},
  volume={47},
  pages={711-730}
}
We establish two new lower bounds for the halfspace range searching problem: Given a set of <i>n</i> points in ℜ<sup><i>d</i></sup>, where each point is associated with a weight from a commutative semigroup, compute the semigroup sum of the weights of the points lying within any query halfspace. Letting $m$ denote the space requirements, we prove a lower bound for general semigroups of Ω(<i>n</i><sup>1-1/(<i>d</i>+1)</sup>/<i>m</i><sup>1/(<i>d</i>+1)</sup>) and for integral semigroups of Ω(<i>n… CONTINUE READING

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