Voronoi diagrams, diameter and distance oracles for planar graphs

Computing distances in graphs is a fundamental and important problem. In this talk I will survey some older and newer results concerning the computation of distances in planar graphs. I then plan to go into some of the details of efficiently constructing weighted Voronoi diagrams for planar graphs. I will also discuss two applications: computing the diameter in O(n^{5/3}) time, and exact distance oracles with O(n^{3/2}) space and O(log n) query time.

 

Based on joint works with Pawel Gawrychowski, Haim Kaplan, Micha Sharir, and Oren Weimann.