A note on dichotomies for metric transforms
Metric Geometry
2011-02-10 v1
Abstract
We show that for every nondecreasing concave function w:R+ --> R+ with w(0)=0, either every finite metric space embeds with distortion arbitrarily close to 1 into a metric space of the form (X,w o d) for some metric d on X, or there exists a=a(w)>0 and n_0=n_0(w)\in N such that for all n>n_0, any embedding of {0,...,n} into a metric space of the form (X,w o d) incurs distortion at least n^a.
Keywords
Cite
@article{arxiv.1102.1800,
title = {A note on dichotomies for metric transforms},
author = {Manor Mendel and Assaf Naor},
journal= {arXiv preprint arXiv:1102.1800},
year = {2011}
}
Comments
7 pages