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

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

2004-07-15

arxiv.org/abs/math/0407278v1

European J. Combinatorics 26(8): 1180-1190,2005

Mathematics

Metric Geometry

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

Scientific paper

10.1016/j.ejc.2004.07.002

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.

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