Distance Oracles Beyond The Thorup-Zwick Bound

We give the first improvement to the space/approximation trade-off of distance oracles since the seminal result of Thorup and Zwick. For unweighted undirected graphs, our distance oracle has size O(n(5/3)) and, when queried about vertices at distance d, returns a path of length at most 2d + 1. For weighted undirected graphs with m = n(2)/alpha edges, our distance oracle has size O(n(2)/(3)root alpha) and returns a factor 2 approximation. Based on a plausible conjecture about the hardness of set intersection queries, we show that a 2- approximate distance oracle requires space (Omega) over tilde (n(2)/root alpha). For unweighted graphs, this implies a (Omega) over tilde (n(1.5)) space lower bound to achieve approximation 2d + 1.