On the impossibility of dimension reduction for doubling subsets of lP

Yair Bartal, Lee Ad Gottlieb, Ofer Neiman

Research output: Contribution to journalArticlepeer-review

3 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 point set, 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 dp with distortion D must have D ≥ (( log n d ) 1 2 â'1p ).

Original languageEnglish
Pages (from-to)1207-1222
Number of pages16
JournalSIAM Journal on Discrete Mathematics
Volume29
Issue number3
DOIs
StatePublished - 1 Jan 2015

Keywords

  • Doubling dimension
  • Embeddings
  • Laakso graph

ASJC Scopus subject areas

  • Mathematics (all)

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