Given an unweighted tree $T=(V,E)$ what is the minimum number of distance oracles that allow to detect the position in the graph of every node $v$?
A distance oracle is "special node" $u$ of the graph that represents a function $d(u,v)$ giving the distance from $u$ to $v$ in constant time.
I have the intuition that this problem is strictly related to all pair shortest path problem, in particular to the Dijkstra algorithm, but can't find a valid algorithm to detect the oracles. Also a backtracking procedure comes to mind for this kind of problem. Maybe you have a better intuition.