Quasi-optimal upper bounds for simplex range searching and new zone theorems

@article{Chazelle1990QuasioptimalUB,
  title={Quasi-optimal upper bounds for simplex range searching and new zone theorems},
  author={Bernard Chazelle and Micha Sharir and Emo Welzl},
  journal={Algorithmica},
  year={1990},
  volume={8},
  pages={407-429}
}
This paper presents quasi-optimal upper bounds for simplex range searching. The problem is to preprocess a setP ofn points in ℜd so that, given any query simplexq, the points inP ∩q can be counted or reported efficiently. Ifm units of storage are available (n <m <n d ), then we show that it is possible to answer any query inO(n 1+ɛ/m 1/d ) query time afterO(m 1+ɛ) preprocessing. This bound, which holds on a RAM or a pointer machine, is almost tight. We also show how to achieveO(logn) query time… CONTINUE READING
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