Metric structures in L1: Dimension, snowflakes, and average distortion
James R. Lee, Manor Mendel, Assaf Naor
Abstract
We study the metric properties of finite subsets of L1. 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 L1.
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