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

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)454-473
Number of pages20
JournalSIAM Journal on Discrete Mathematics
Issue number1
StatePublished - 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. 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 ( ‡Edgestream Partners L. P., Princeton, NJ 08540 ( §Google Inc., Mountain View, CA 94043 ( ¶Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213 (anupamg@ ‖MIT, Cambridge, MA 02139 ( #Department of Computer Science, University of Haifa, Haifa, Israel ( ††Technische Universität München, München, Germany ( ‡‡CMU, Pittsburgh, PA 15213 (

Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics


  • Approximation algorithms
  • Distortion
  • Line
  • Metric embeddings
  • Sphere

ASJC Scopus subject areas

  • Mathematics (all)


Dive into the research topics of 'Approximation algorithms for low-distortion embeddings into low-dimensional spaces'. Together they form a unique fingerprint.

Cite this