The Minimum Spanning Tree Problem: Difference between revisions
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=External= | |||
* https://www.coursera.org/learn/algorithms-greedy/lecture/9D5ML/mst-problem-definition | |||
* https://www.coursera.org/learn/algorithms-greedy/lecture/Wt9aw/msts-state-of-the-art-and-open-questions-advanced-optional | |||
=Internal= | =Internal= | ||
* [[Algorithms#Greedy_Algorithms|Algorithms]] | * [[Algorithms#Greedy_Algorithms|Greedy Algorithms]] | ||
* [[Graph_Concepts#Minimum_Spanning_Tree_.28MST.29|Graph Concepts]] | |||
* [[Prim%27s_Algorithm|Prim's Algorithm]] | * [[Prim%27s_Algorithm|Prim's Algorithm]] | ||
* [[Kruskal%27s_Algorithm|Kruskal's Algorithm]] | * [[Kruskal%27s_Algorithm|Kruskal's Algorithm]] | ||
* [[The Optimal Branching Problem]] | |||
=Overview= | |||
We discuss the minimum spanning problem in the context of [[Graph_Concepts#Undirected_Graph|undirected]] graphs. The same problem can be discussed for [[Graph_Concepts#Directed_Graph|directed]] graphs but in that case it is referred to as the [[The Optimal Branching Problem|Optimal Branching Problem]]. | |||
=The Problem= | =The Problem= | ||
Given an [[Graph_Concepts#Undirected_Graph|undirected]] graph G=(V, E) | Given an [[Graph_Concepts#Undirected_Graph|undirected]] graph G=(V, E) and a positive or negative cost c<sub>e</sub> for each edge e ∈ E, find the [[Graph_Concepts#Spanning_Tree_Cost|minimum cost]] [[Graph_Concepts#Spanning_Trees|spanning tree]] T ⊆ E (MST). | ||
=Algorithms= | |||
The minimum spanning tree problem is solved by [[Algorithms#Greedy_Algorithms|greedy algorithms]]: | |||
==Prim's Algorithm== | |||
{{Internal|Prim%27s_Algorithm#Overview|Prim's Algorithm}} | |||
==Kruskal's Algorithm== | |||
{{Internal|Kruskal%27s_Algorithm|Kruskal's Algorithm}} | |||
Latest revision as of 20:07, 22 October 2021
External
- https://www.coursera.org/learn/algorithms-greedy/lecture/9D5ML/mst-problem-definition
- https://www.coursera.org/learn/algorithms-greedy/lecture/Wt9aw/msts-state-of-the-art-and-open-questions-advanced-optional
Internal
Overview
We discuss the minimum spanning problem in the context of undirected graphs. The same problem can be discussed for directed graphs but in that case it is referred to as the Optimal Branching Problem.
The Problem
Given an undirected graph G=(V, E) and a positive or negative cost ce for each edge e ∈ E, find the minimum cost spanning tree T ⊆ E (MST).
Algorithms
The minimum spanning tree problem is solved by greedy algorithms: