Past exam of the short options course of the University of Oxford / 2017 / 7 / a / iii

A shortest-path tree rooted at $v$ is a spanning tree $T$ of $G$ for which the unique $vu$-path in $T$ is a $w$-shortest $vu$-path in $G$ for every vertex $u$. It simultaneously realizes all distances from the root. It need not be a minimum spanning tree, which minimizes total tree weight instead.