A Spectral Approach to Lower Bounds with Applications to Geometric Searching

@inproceedings{SIAMJ1998ASA,
  title={A Spectral Approach to Lower Bounds with Applications to Geometric Searching},
  author={C SIAMJ.},
  year={1998}
}
  • C SIAMJ.
  • Published 1998
We establish a nonlinear lower bound for halfplane range searching over a group. Specifically, we show that summing up the weights of n (weighted) points within n halfplanes requires Ω(n logn) additions and subtractions. This is the first nontrivial lower bound for range searching over a group. By contrast, range searching over a semigroup (which forbids subtractions) is almost completely understood. Our proof has two parts. First, we develop a general, entropy-based method for relating the… CONTINUE READING
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