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(n⁵/³) and, when queried about vertices at distance d, returns a path of length at most 2d +1. For weighted undirected graphs with m = n²/a edges, our distance oracle has size O(n²/ 3 v α) 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 ~Ω&(n²/ v α). For unweighted graphs, this implies a ~Ω&(n^1.5) space lower bound to achieve approximation 2d + 1.