Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

All Pairs Shortest Paths in Sparse Graphs

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

Years and Authors of Summarized Original Work

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 \(\vert V \vert = n,\vert E\vert = m\)


Quickest route Shortest route 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.EECS DepartmentUniversity of MichiganAnn Arbor, MIUSA