Proximity algorithms for nearly doubling spaces

Lee Ad Gottlieb; Robert Krauthgamer

doi:10.1137/120874242

Proximity algorithms for nearly doubling spaces

Lee Ad Gottlieb, Robert Krauthgamer

Ariel University, Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce a new problem in the study of doubling spaces: Given a point set S and a target dimension d, remove from S the fewest number of points so that the remaining set has doubling dimension at most d. We present a bicriteria approximation for this problem and extend this algorithm to solve a group of proximity problems.

Original language	English
Pages (from-to)	1759-1769
Number of pages	11
Journal	SIAM Journal on Discrete Mathematics
Volume	27
Issue number	4
DOIs	https://doi.org/10.1137/120874242
State	Published - 2013

Keywords

All points nearest neighbor
Approximate distance oracle
Approximate minimum spanning tree
Doubling dimension
Metric spanners

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1137/120874242

Cite this

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title = "Proximity algorithms for nearly doubling spaces",

abstract = "We introduce a new problem in the study of doubling spaces: Given a point set S and a target dimension d, remove from S the fewest number of points so that the remaining set has doubling dimension at most d. We present a bicriteria approximation for this problem and extend this algorithm to solve a group of proximity problems.",

keywords = "All points nearest neighbor, Approximate distance oracle, Approximate minimum spanning tree, Doubling dimension, Metric spanners",

author = "Gottlieb, \{Lee Ad\} and Robert Krauthgamer",

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year = "2013",

doi = "10.1137/120874242",

language = "الإنجليزيّة",

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AU - Gottlieb, Lee Ad

AU - Krauthgamer, Robert

N1 - Israel Science Foundation [452/08]; Minerva grantThis work was supported in part by the Israel Science Foundation (grant 452/08) and by a Minerva grant.

PY - 2013

Y1 - 2013

N2 - We introduce a new problem in the study of doubling spaces: Given a point set S and a target dimension d, remove from S the fewest number of points so that the remaining set has doubling dimension at most d. We present a bicriteria approximation for this problem and extend this algorithm to solve a group of proximity problems.

AB - We introduce a new problem in the study of doubling spaces: Given a point set S and a target dimension d, remove from S the fewest number of points so that the remaining set has doubling dimension at most d. We present a bicriteria approximation for this problem and extend this algorithm to solve a group of proximity problems.

KW - All points nearest neighbor

KW - Approximate distance oracle

KW - Approximate minimum spanning tree

KW - Doubling dimension

KW - Metric spanners

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U2 - 10.1137/120874242

DO - 10.1137/120874242

M3 - مقالة

SN - 0895-4801

VL - 27

SP - 1759

EP - 1769

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 4

ER -

Proximity algorithms for nearly doubling spaces

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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