Embedding the diamond graph in Lp and dimension reduction in L1

James R. Lee, Assaf Naor

Research output: Contribution to journalArticle

Abstract

We show that any embedding of the level k diamond graph of Newman and Rabinovich [NR] into Lp, 1 < p ≤ 2, requires distortion at least √k(p - 1) + 1. An immediate corollary is that there exist arbitrarily large n-point sets X ⊆ L1 such that any D-embedding of X into ℓ1d requires d ≥ n Ω(1/D2). This gives a simple proof of a recent result of Brinkman and Charikar [BrC] which settles the long standing question of whether there is an L1 analogue of the Johnson-Lindenstrauss dimension reduction lemma [JL].

Original languageEnglish (US)
Pages (from-to)745-747
Number of pages3
JournalGeometric and Functional Analysis
Volume14
Issue number4
DOIs
StatePublished - 2004

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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