On the impossibility of dimension reduction for doubling subsets of ℓp

Yair Bartal, Lee Ad Gottlieb, Ofer Neiman

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

4 Scopus citations

Abstract

A major open problem in the field of metric embedding is the existence of dimension reduction for n-point subsets of Euclidean space, such that both distortion and dimension depend only on the doubling constant of the pointset, and not on its cardinality. In this paper, we negate this possibility for ℓp spaces with p > 2. In particular, we introduce an n-point subset of ℓp with doubling constant O(1), and demonstrate that any embedding of the set into ℓpd with distortion D must have D ≥ Ω ((c log n/d 1/2-1/p Copyright is held by the owner/author(s).

Original languageEnglish
Title of host publicationProceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014
PublisherAssociation for Computing Machinery
Pages60-66
Number of pages7
ISBN (Print)9781450325943
DOIs
StatePublished - 1 Jan 2014
Event30th Annual Symposium on Computational Geometry, SoCG 2014 - Kyoto, Japan
Duration: 8 Jun 201411 Jun 2014

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Conference

Conference30th Annual Symposium on Computational Geometry, SoCG 2014
Country/TerritoryJapan
CityKyoto
Period8/06/1411/06/14

Keywords

  • Dimension reduction
  • Doubling metrics
  • Embedding

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