# Nearly Tight Low Stretch Spanning Trees

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Ofer Neiman, Courant Institute, NYU
Fine Hall 224

We prove that any graph $G$ on $n$ vertices has a distribution over its spanning trees such that for any edge $(u,v)$ the expected stretch $E_T[d_T(u,v)]$ 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. Joint work with Ittai Abraham and Yair Bartal