English

Metric structures in L_1: Dimension, snowflakes, and average distortion

Metric Geometry 2007-05-23 v1 Combinatorics

Abstract

We study the metric properties of finite subsets of L_1. The analysis of such metrics is central to a number of important algorithmic problems involving the cut structure of weighted graphs, including the Sparsest Cut Problem, one of the most compelling open problems in the field of approximation algorithms. Additionally, many open questions in geometric non-linear functional analysis involve the properties of finite subsets of L_1.

Keywords

Cite

@article{arxiv.math/0407278,
  title  = {Metric structures in L_1: Dimension, snowflakes, and average distortion},
  author = {James R. Lee and Manor Mendel and Assaf Naor},
  journal= {arXiv preprint arXiv:math/0407278},
  year   = {2007}
}

Comments

9 pages, 1 figure. To appear in European Journal of Combinatorics. Preliminary version appeared in LATIN '04

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