Shortest Path in a Graph: Difference between revisions
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=The Problem= | =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 has a '''non-negative''' length ℓ<sub>e</sub>, and a [[Graph_Concepts#Source_Vertex|source vertex]] s, compute for | 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 has a '''non-negative''' length ℓ<sub>e</sub>, and a [[Graph_Concepts#Source_Vertex|source vertex]] s, compute for | ||
=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 19:44, 14 October 2021
External
- https://www.coursera.org/learn/algorithms-graphs-data-structures/lecture/ZAaJA/bfs-and-shortest-paths
- 5 Ways to Find the Shortest Path in a Graph https://betterprogramming.pub/5-ways-to-find-the-shortest-path-in-a-graph-88cfefd0030f
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.
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 has a non-negative length ℓe, and a source vertex s, compute for