Nearly Tight Low Stretch Spanning Trees
Ittai Abraham, Yair Bartal, and Ofer Neiman

TL;DR
This paper introduces a method to construct low-stretch spanning trees with nearly tight bounds, using a novel approach involving highway construction and a strong diameter decomposition, improving graph spanning tree efficiency.
Contribution
It presents a new probabilistic approach for building low-stretch spanning trees with nearly optimal bounds, utilizing highway networks and a strong diameter decomposition.
Findings
Expected stretch bounded by O( log n) for any graph.
New probabilistic decomposition theorem for strong diameter.
Method applicable to all graphs with n points.
Abstract
We prove that any graph with points has a distribution over spanning trees such that for any edge the expected stretch is bounded by . Our result is obtained via a new approach of building ``highways'' between portals and a new strong diameter probabilistic decomposition theorem.
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Optimization and Search Problems · Computational Geometry and Mesh Generation
