Title: Low Dimensional Embedding of Doubling Metrics
Author: Ofer Neiman
Abstract: We study several embeddings of doubling metrics into low dimensional normed spaces,
in particular into L_2 and L_\infty. Doubling metrics are a robust class of metric
spaces that have low intrinsic dimension, and often occur in applications. Understanding the
dimension required for a concise representation of such metrics is a fundamental open problem
in the area of metric embedding. Here we show that the n-vertex Laakso graph can be embedded
into constant dimensional L_2 with the best possible distortion, which has implications for
possible approaches to the above problem.
Since arbitrary doubling metrics require high distortion for embedding into L_2 and even into
L_1, we turn to the L_\infty space that enables us to obtain arbitrarily small distortion.
We show embeddings of doubling metrics and their "snowflakes" into low dimensional L_\infty
space that simplify and extend previous results.