Fast construction of nets in low dimensional metrics, and their applications

Sariel Har-Peled; Manor Mendel

doi:10.1145/1064092.1064117

Fast construction of nets in low dimensional metrics, and their applications

Sariel Har-Peled, Manor Mendel

Research output: Contribution to conference › Paper › peer-review

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.

Original language	English
Pages	150-158
Number of pages	9
DOIs	https://doi.org/10.1145/1064092.1064117
State	Published - 2005
Externally published	Yes
Event	21st Annual Symposium on Computational Geometry, SCG'05 - Pisa, Italy Duration: 6 Jun 2005 → 8 Jun 2005

Conference

Conference	21st Annual Symposium on Computational Geometry, SCG'05
Country/Territory	Italy
City	Pisa
Period	6/06/05 → 8/06/05

Keywords

Approximate distance oracle
Approximate nearest neighbor search
Compact representation scheme
Doubling metrics
Spanners
Well separated pair decomposition

Access to Document

10.1145/1064092.1064117

Cite this

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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.",

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AB - 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.

KW - Approximate distance oracle

KW - Approximate nearest neighbor search

KW - Compact representation scheme

KW - Doubling metrics

KW - Spanners

KW - Well separated pair decomposition

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T2 - 21st Annual Symposium on Computational Geometry, SCG'05

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ER -

Fast construction of nets in low dimensional metrics, and their applications

Abstract

Conference

Keywords

Access to Document

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