I would like to find the "optimal" shortest path tree (SPT) in some undirected weighted graph. As "optimal" SPT, I mean so its maximal path from root to leaf is minimal from any other potential SPTs.
It is quite easy to find SPT from 1 root via Dijkstra's algorithm. So I can run Dijkstra from all vertices and find the "optimal" SPT and its root.
Is there any faster algorithm?