Shortest Path in a Graph: Difference between revisions

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=Overview=
=Overview=
There are several algorithms that compute the shortest path between two vertices in a graph, and they can be used or not depending on the characteristics of the graph, such as whether is directed or undirected, the edges have weights, the weights are negative or not.
There are several algorithms that compute the shortest path between two vertices in a graph, and they can be used or not depending on the characteristics of the graph, such as whether is directed or undirected, the edges have weights, the weights are negative or not.
=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<sub>e</sub>, and a [[Graph_Concepts#Source_Vertex|source vertex]] s, compute for each v ∈ V the length of the shortest path s → v L(v).


=Shortest Path Algorithms=
=Shortest Path Algorithms=
* [[Breadth-First Search-based Shortest Path Algorithm]]
* [[Breadth-First Search-based Shortest Path Algorithm]]
* [[Dijkstra's Shortest-Path Algorithm]]
* [[Dijkstra's Shortest-Path Algorithm]]

Revision as of 19:46, 14 October 2021

External

Internal

Overview

There are several algorithms that compute the shortest path between two vertices in a graph, and they can be used or not depending on the characteristics of the graph, such as whether is directed or undirected, the edges have weights, the weights are negative or not.

Shortest Path Algorithms