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 $d$, ...

An approximate distance oracle is a succinct data structure that provides fast answers to distance queries between any two nodes of a given graph.

In this paper we consider approximate distance oracles for general undirected graphs with non-negative ...

Thorup and Zwick [2001a] proposed a landmark distance oracle with the following properties. Given an n-vertex undirected graph G = (V, E) and a parameter k = 1, 2, …, their oracle has size O(kn^{1 + 1/k}), and upon a query (u, v) it constructs a path Π ...