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

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

Informatics 14 - Associate Professorship of Theoretical Computer Science

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

2 Scopus citations

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

Keywords

Approximation algorithms
Distortion
Line
Metric embeddings
Sphere

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10.1137/17M1113527

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title = "Approximation algorithms for low-distortion embeddings into low-dimensional spaces",

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.",

keywords = "Approximation algorithms, Distortion, Line, Metric embeddings, Sphere",

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

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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, And 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

U2 - 10.1137/17M1113527

DO - 10.1137/17M1113527

M3 - Article

AN - SCOPUS:85064382033

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EP - 473

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 1

ER -

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

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Keywords

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