Fast Construction of Nets in Low-Dimensional Metrics and Their Applications

@article{HarPeled2006FastCO,
  title={Fast Construction of Nets in Low-Dimensional Metrics and Their Applications},
  author={Sariel Har-Peled and M. Mendel},
  journal={SIAM J. Comput.},
  year={2006},
  volume={35},
  pages={1148-1184}
}
We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This data-structure is then applied to obtain improved algorithms for the following problems: approximate nearest neighbor search, well-separated pair decomposition, spanner construction, compact representation scheme, doubling measure, and computation of the (approximate) Lipschitz constant of a function. In all cases, the running (preprocessing) time is near… 

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