# Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

# Approximate Distance Oracles with Improved Query Time

• Christian Wulff-Nilsen
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_568-1

## Years and Authors of Summarized Original Work

2013; Wulff-Nilsen

## Problem Definition

This problem is concerned with obtaining a compact data structure capable of efficiently reporting approximate shortest path distance queries in a given undirected edge-weighted graph G = (V, E). If the query time is independent (or nearly independent) of the size of G, we refer to the data structure as an approximate distance oracle for G. For vertices u and v in G, we denote by dG(u, v) the shortest path distance between u and v in G. For a given stretch parameter δ ≥ 1, we call the oracle δ-approximate if for all vertices u and v in G, $$d_{G}(u,v) \leq \tilde{ d}_{G}(u,v) \leq \delta d_{G}(u,v)$$

## Keywords

Approximate distance oracle Shortest paths Graphs Query time
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