# 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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