Dijkstra's Shortest-Path Algorithm

Internal

• Shortest Path in a Graph

The Problem

The single-source shortest paths is formally defined as follows: given a directed graph G=(V, E) , with n = │V│ and m=│E│, where each edge e has a non-negative length ℓ_e, and a source vertex s, compute for each v ∈ V the length L(v) of the shortest path s → v.

The assumption that the length is non-negative is important. Dijkstra's shortest-path algorithm does not work correctly in presence of negative length edges.

Speed Up

The Dijkstra's algorithm can be speed up with the use of a heap.