Nearly Tight Low Stretch Spanning Trees

Ittai Abraham; Yair Bartal; Ofer Neiman

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arXiv · 0808.2017

Nearly Tight Low Stretch Spanning Trees

Ittai Abraham·Yair Bartal·Ofer Neiman

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Abstract

We prove that any graph $G$ with $n$ points has a distribution $\mathcal{T}$ over spanning trees such that for any edge $(u,v)$ the expected stretch $E_{T \sim \mathcal{T}}[d_T(u,v)/d_G(u,v)]$ is bounded by $\tilde{O}(\log n)$. 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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Ittai Abraham, Yair Bartal, Ofer Neiman. 2008-08-14. Nearly Tight Low Stretch Spanning Trees. https://arxiv.org/abs/0808.2017

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