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

Funding Information:
∗Received by the editors January 25, 2017; accepted for publication (in revised form) January 22, 2019; published electronically March 7, 2019. http://www.siam.org/journals/sidma/33-1/M111352.html Funding: The second, sixth, and seventh authors were supported by NSF ITR grants CCR-0085982 and CCR-0122581. The seventh author was also supported by NSF and NSF CCF 04-30751.

Funding Information:
The eighth author was supported by the Paris Kanellakis Fellowship Fund, the Alexandros S. Onassis Public Benefit Foundation, and by the National Science Foundation under grant CCF-1423230 and award CAREER-1453472. †Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607 (sidiropo@gmail.com). ‡Edgestream Partners L. P., Princeton, NJ 08540 (mihai@mit.edu). §Google Inc., Mountain View, CA 94043 (kedar@cs.cmu.edu). ¶Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213 (anupamg@ cs.cmu.edu). ‖MIT, Cambridge, MA 02139 (indyk@mit.edu). #Department of Computer Science, University of Haifa, Haifa, Israel (yuri@cslx.haifa.ac.il). ††Technische Universität München, München, Germany (harald.raecke@tum.de). ‡‡CMU, Pittsburgh, PA 15213 (ravi@andrew.cmu.edu).

Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics

Keywords

Approximation algorithms
Distortion
Line
Metric embeddings
Sphere

ASJC Scopus subject areas

Mathematics (all)

Access to Document

10.1137/17M1113527

Cite this

@article{b708563ade3c4b20af8efc163349c4ee,

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.}",

note = "Funding Information: ∗Received by the editors January 25, 2017; accepted for publication (in revised form) January 22, 2019; published electronically March 7, 2019. http://www.siam.org/journals/sidma/33-1/M111352.html Funding: The second, sixth, and seventh authors were supported by NSF ITR grants CCR-0085982 and CCR-0122581. The seventh author was also supported by NSF and NSF CCF 04-30751. Funding Information: The eighth author was supported by the Paris Kanellakis Fellowship Fund, the Alexandros S. Onassis Public Benefit Foundation, and by the National Science Foundation under grant CCF-1423230 and award CAREER-1453472. †Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607 (sidiropo@gmail.com). ‡Edgestream Partners L. P., Princeton, NJ 08540 (mihai@mit.edu). §Google Inc., Mountain View, CA 94043 (kedar@cs.cmu.edu). ¶Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213 (anupamg@ cs.cmu.edu). ‖MIT, Cambridge, MA 02139 (indyk@mit.edu). #Department of Computer Science, University of Haifa, Haifa, Israel (yuri@cslx.haifa.ac.il). ††Technische Universit{\"a}t M{\"u}nchen, M{\"u}nchen, Germany (harald.raecke@tum.de). ‡‡CMU, Pittsburgh, PA 15213 (ravi@andrew.cmu.edu). Publisher Copyright: {\textcopyright} 2019 Society for Industrial and Applied Mathematics",

year = "2019",

doi = "10.1137/17M1113527",

language = "English",

volume = "33",

pages = "454--473",

journal = "SIAM Journal on Discrete Mathematics",

issn = "0895-4801",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "1",

}

TY - JOUR

T1 - Approximation algorithms for low-distortion embeddings into low-dimensional spaces

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.

N1 - Funding Information: ∗Received by the editors January 25, 2017; accepted for publication (in revised form) January 22, 2019; published electronically March 7, 2019. http://www.siam.org/journals/sidma/33-1/M111352.html Funding: The second, sixth, and seventh authors were supported by NSF ITR grants CCR-0085982 and CCR-0122581. The seventh author was also supported by NSF and NSF CCF 04-30751. Funding Information: The eighth author was supported by the Paris Kanellakis Fellowship Fund, the Alexandros S. Onassis Public Benefit Foundation, and by the National Science Foundation under grant CCF-1423230 and award CAREER-1453472. †Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607 (sidiropo@gmail.com). ‡Edgestream Partners L. P., Princeton, NJ 08540 (mihai@mit.edu). §Google Inc., Mountain View, CA 94043 (kedar@cs.cmu.edu). ¶Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213 (anupamg@ cs.cmu.edu). ‖MIT, Cambridge, MA 02139 (indyk@mit.edu). #Department of Computer Science, University of Haifa, Haifa, Israel (yuri@cslx.haifa.ac.il). ††Technische Universität München, München, Germany (harald.raecke@tum.de). ‡‡CMU, Pittsburgh, PA 15213 (ravi@andrew.cmu.edu). Publisher Copyright: © 2019 Society for Industrial and Applied Mathematics

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 - http://www.scopus.com/inward/record.url?scp=85064382033&partnerID=8YFLogxK

U2 - 10.1137/17M1113527

DO - 10.1137/17M1113527

M3 - Article

AN - SCOPUS:85064382033

SN - 0895-4801

VL - 33

SP - 454

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this