Lower-Stretch Spanning Trees

TL;DR

This paper proves that every weighted graph has a spanning tree with low average stretch, and provides an efficient construction method for such trees, improving understanding of graph structures and algorithms.

Contribution

It introduces a method to find low-stretch spanning trees with optimal bounds and an efficient algorithm to construct them in near-linear time.

Findings

Existence of spanning trees with average stretch O((log n log log n)^2)

Efficient construction algorithm running in O(m log^2 n) time

Advances in graph algorithms for low-stretch trees

Abstract

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).