We prove that every weighted graph contains a spanning tree subgraph of average stretch O((log n log log n)^2). Moreover, we show how to construct such a tree in time O(m log^2 n).
Cite
@article{arxiv.cs/0411064,
title = {Lower-Stretch Spanning Trees},
author = {Michael Elkin and Yuval Emek and Daniel A. Spielman and Shang-Hua Teng},
journal= {arXiv preprint arXiv:cs/0411064},
year = {2007}
}