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 (US)
Pages (from-to)454-473
Number of pages20
JournalSIAM Journal on Discrete Mathematics
Issue number1
StatePublished - 2019


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

ASJC Scopus subject areas

  • General Mathematics


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