Lower-Stretch Spanning Trees
Michael Elkin, Yuval Emek, Daniel A. Spielman, Shang-Hua Teng

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).
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Taxonomy
TopicsOptimization and Search Problems · Complexity and Algorithms in Graphs · Advanced Graph Theory Research
