Approximation algorithms for low-distortion embeddings into low-dimensional spaces

Anastasios Sidiropoulos; Mihai Badoiu; Kedar Dhamdhere; Anupam Gupta; Piotr Indyk; Yuri Rabinovich; Harald Racke; R. Ravi

doi:10.1137/17M1113527

Approximation algorithms for low-distortion embeddings into low-dimensional spaces

Anastasios Sidiropoulos
, Mihai Badoiu
, Kedar Dhamdhere
, Anupam Gupta
, Piotr Indyk
, Yuri Rabinovich
, Harald Racke
, R. Ravi

Department of Computer Science

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

Abstract

We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the 2-dimensional plane. Among other results, we give an O(n)approximation algorithm for the problem of finding a line embedding of a metric induced by a given unweighted graph, that minimizes the (standard) multiplicative distortion. We give an improved Õ(n¹/³) approximation for the case of metrics induced by unweighted trees.

Original language	English
Pages (from-to)	454-473
Number of pages	20
Journal	SIAM Journal on Discrete Mathematics
Volume	33
Issue number	1
DOIs	https://doi.org/10.1137/17M1113527
State	Published - 2019

Bibliographical note

Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics

Keywords

Approximation algorithms
Distortion
Line
Metric embeddings
Sphere

ASJC Scopus subject areas

General Mathematics

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10.1137/17M1113527

Cite this

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abstract = "We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the 2-dimensional plane. Among other results, we give an O(n)approximation algorithm for the problem of finding a line embedding of a metric induced by a given unweighted graph, that minimizes the (standard) multiplicative distortion. We give an improved {\~O}(n1/3) approximation for the case of metrics induced by unweighted trees.",

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author = "Anastasios Sidiropoulos and Mihai Badoiu and Kedar Dhamdhere and Anupam Gupta and Piotr Indyk and Yuri Rabinovich and Harald Racke and R. Ravi",

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AU - Sidiropoulos, Anastasios

AU - Badoiu, Mihai

AU - Dhamdhere, Kedar

AU - Gupta, Anupam

AU - Indyk, Piotr

AU - Rabinovich, Yuri

AU - Racke, Harald

AU - Ravi, R.

PY - 2019

Y1 - 2019

N2 - We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the 2-dimensional plane. Among other results, we give an O(n)approximation algorithm for the problem of finding a line embedding of a metric induced by a given unweighted graph, that minimizes the (standard) multiplicative distortion. We give an improved Õ(n1/3) approximation for the case of metrics induced by unweighted trees.

AB - We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the 2-dimensional plane. Among other results, we give an O(n)approximation algorithm for the problem of finding a line embedding of a metric induced by a given unweighted graph, that minimizes the (standard) multiplicative distortion. We give an improved Õ(n1/3) approximation for the case of metrics induced by unweighted trees.

KW - Approximation algorithms

KW - Distortion

KW - Line

KW - Metric embeddings

KW - Sphere

UR - https://www.scopus.com/pages/publications/85064382033

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DO - 10.1137/17M1113527

M3 - Article

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JF - SIAM Journal on Discrete Mathematics

IS - 1

ER -

Approximation algorithms for low-distortion embeddings into low-dimensional spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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