# Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

# All Pairs Shortest Paths in Sparse Graphs

• Seth Pettie
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_11-2

2004; Pettie

## Problem Definition

Given a communications network or road network, one of the most natural algorithmic questions is how to determine the shortest path from one point to another. The all pairs shortest path problem (APSP) is, given a directed graph G = (V, E, l), to determine the distance and shortest path between every pair of vertices, where $$\vert V \vert = n,\vert E\vert = m$$

## Keywords

Quickest route Shortest route
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