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

Sariel Har-Peled·Manor Mendel
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Abstract

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, compact representation scheme, doubling measure, and computation of the (approximate) Lipschitz constant of a function. In all cases, the running (preprocessing) time is near-linear and the space being used is linear.

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Sariel Har-Peled, Manor Mendel. 2005-08-22. Fast Construction of Nets in Low Dimensional Metrics, and Their Applications. https://doi.org/10.1137/s0097539704446281

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