Metric Embeddings - Beyond One-Dimensional Distortion

Abstract

Metric spaces and their embeddings have recently played a prominent role in the development of new algorithms. So far, most of the emphasis was on embeddings that preserve pairwise distances. A very intriguing concept introduced by Feige [Fei00], allows us to quantify the extent to which higher-dimensional structures are preserved by a given embedding. We investigate this concept for several basic graph families such as paths, trees, cubes and expanders.

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Document Details

Document Type
Technical Report
Publication Date
May 15, 2002
Accession Number
ADA619309

Entities

People

  • Avner Magen
  • Nathan Linial
  • Robert Krauthgamer

Organizations

  • University of California, Berkeley

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Aspect Ratio
  • Banach Space
  • California
  • Computer Science
  • Computers
  • Diameters
  • Distortion
  • Electronic Mail
  • Embedding
  • Equations
  • Geometry
  • Hilbert Space
  • Inequalities
  • Probability
  • Trees (Data Structures)
  • Two Dimensional

Fields of Study

  • Computer science

Readers

  • Computer Vision.
  • Theoretical Analysis.
  • Urban Planning and Geography.

Technology Areas

  • Space