## Fast construction of nets in low dimensional metrics, and their applications (2005)

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Venue: | SIAM J. Comput |

Citations: | 98 - 11 self |

### BibTeX

@INPROCEEDINGS{Har-peled05fastconstruction,

author = {Sariel Har-peled and Manor Mendel},

title = {Fast construction of nets in low dimensional metrics, and their applications},

booktitle = {SIAM J. Comput},

year = {2005},

pages = {150--158}

}

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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, 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 linear and the space being used is linear. 1