# Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

# Hub Labeling (2-Hop Labeling)

• Daniel Delling
• Andrew V. Goldberg
• Renato F. Werneck
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_580

## Years and Authors of Summarized Original Work

• 2003; Cohen, Halperin, Kaplan, Zwick

• 2012; Abraham, Delling, Goldberg, Werneck

• 2013; Akiba, Iwata, Yoshida

• 2014; Delling, Goldberg, Pajor, Werneck

• 2014; Delling, Goldberg, Savchenko, Werneck

## Problem Definition

Given a directed graph G = (V, A) (with n =| V | and m =| A | ) with a length function : AR+ and a pair of vertices s, t, a distance oracle returns the distance dist(s, t) from s to t. A labeling algorithm [18] implements distance oracles in two stages. The preprocessing stage computes a label for each vertex of the input graph. Then, given s and t, the query stage computes dist(s, t) using only the labels of s and t; the query does not explicitly use G and .

Hub labeling (HL) (or 2-hop labeling) is a special kind of labeling algorithm. The label L( v) of a vertex v consists of two parts: the forward label L f( v) is a collection of vertices w with their distances dist( v, w) from v, while the backward label L b( v) is a collection...

## Keywords

Distance oracles Labeling algorithms Shortest paths
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