I will explain how orthogonal range searching has been useful to
improve the running time of algorithms solving the following
problems:
a) Computing the sum of the distances between all pairs of vertices
in a graph of bounded treewidth.
b) Computing the dilation of a geometric graph of bounded treewidth.
c) Computing an optimal pricing in the Stackelberg shortest path tree
game.
(Parts a) and b) are joint work with Christian Knauer.)