Nearly Tight Low Stretch Spanning Trees

Details Nearly Tight Low Stretch Spanning Trees Nearly Tight Low Stretch Spanning Trees

2008-08-14

arxiv.org/abs/0808.2017v1

Computer Science

Data Structures and Algorithms

Scientific paper

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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