Low dimensional embeddings of doubling metrics

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


We study several embeddings of doubling metrics into low dimensional normed spaces, in particular into ℓ2 and ℓ. Doubling metrics are a robust class of metric spaces that have low intrinsic dimension, and often occur in applications. Understanding the dimension required for a concise representation of such metrics is a fundamental open problem in the area of metric embedding. Here we show that the n-vertex Laakso graph can be embedded into constant dimensional ℓ2 with the best possible distortion, which has implications for possible approaches to the above problem. Since arbitrary doubling metrics require high distortion for embedding into ℓ2 and even into ℓ1, we turn to the ℓ space that enables us to obtain arbitrarily small distortion. We show embeddings of doubling metrics and their "snowflakes" into low dimensional ℓ space that simplify and extend previous results.

Original languageEnglish
Title of host publicationApproximation and Online Algorithms - 11th International Workshop, WAOA 2013, Revised Selected Papers
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783319080000
StatePublished - 1 Jan 2014
Event11th International Workshop on Approximation and Online Algorithms, WAOA 2013 - Sophia Antipolis, France
Duration: 5 Sep 20136 Sep 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8447 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference11th International Workshop on Approximation and Online Algorithms, WAOA 2013
CitySophia Antipolis

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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