The Minimum Spanning Tree Problem

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

• Greedy Algorithms
• Graph Concepts
• Prim's Algorithm
• Kruskal's Algorithm
• The Optimal Branching Problem

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 c_e 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:

Prim's Algorithm

Prim's Algorithm

Kruskal's Algorithm

Kruskal's Algorithm