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.