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

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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AU - Dhamdhere, Kedar

AU - Gupta, Anupam

AU - Indyk, Piotr

AU - Rabinovich, Yuri

AU - Racke, Harald

AU - Ravi, And R.

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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

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KW - Metric embeddings

KW - Sphere

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JF - SIAM Journal on Discrete Mathematics

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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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Cite this