Quasisymmetric embeddings, the observable diameter, and expansion properties of graphs

Assaf Naor, Yuval Rabani, Alistair Sinclair

Research output: Contribution to journalArticle

Abstract

It is shown that the edges of any n-point vertex expander can be replaced by new edges so that the resulting graph is an edge expander, and such that any two vertices that are joined by a new edge are at distance O (√log n) in the original graph. This result is optimal, and is shown to have various geometric consequences. In particular, it is used to obtain an alternative perspective on the recent algorithm of Arora et al. [Proceedings of the 36th Annual ACM Symposium on the Theory of Computing, 2004, pp. 222-231.] for approximating the edge expansion of a graph, and to give a nearly optimal lower bound on the ratio between the observable diameter and the diameter of doubling metric measure spaces which are quasisymmetrically embeddable in Hilbert space.

Original languageEnglish (US)
Pages (from-to)273-303
Number of pages31
JournalJournal of Functional Analysis
Volume227
Issue number2
DOIs
StatePublished - Oct 15 2005

Keywords

  • Edge expansion
  • Observable diameter
  • Quasisymmetric embeddings
  • Vertex expansion

ASJC Scopus subject areas

  • Analysis

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