Approximate Distance Oracles with Improved Stretch for Sparse Graphs

Abstract

Thorup and Zwick [19] introduced the notion of approximate distance oracles, a data structure that produces for an n-vertices, m-edges weighted undirected graph \(G=(V,E)\), distance estimations in constant query time. They presented a distance oracle of size \(O(kn^{1+1/k})\) that given a pair of vertices \(u,v \in V\) at distance d(u, v) produces in O(k) time an estimation that is bounded by \((2k-1)d(u,v)\), i.e., a \((2k-1)\)-multiplicative approximation (stretch). Thorup and Zwick [19] presented also a lower bound based on the girth conjecture of Erdős.