Before revision:  As in Cabello's work, our algorithm can also compute the Wiener index of ( sum of all pairwise distances in) a planar graph, within the same bounds  .
After revision:  As in Cabello's work, our algorithm can also compute the Wiener index of ( sum of all pairwise distances in) a planar graph, within the same bound. Our construction of Voronoi diagrams for planar graphs is of independent interest. It has already been used to obtain fast exact distance oracles for planar graphs .