Kruskal's Algorithm

on November 11, 2022 · 3 mins read

Introduction to Kruskal’s Algorithm

Kruskal’s algorithm is an algorithm used to find the minimum spanning tree of a graph. It was first proposed by Joseph Kruskal in 1956 and is one of the most popular algorithms for finding the minimum spanning tree of a graph.

Kruskal’s algorithm is a greedy algorithm, which means that it makes decisions based on the current state of the graph. It starts by looking at the edges of the graph and finding the edge with the lowest weight. It then adds this edge to the minimum spanning tree and moves on to the next edge with the lowest weight until all the edges have been added to the tree.

In this blog post, we will look at Kruskal’s algorithm in detail, including how it works and how to implement it in pseudocode. We will also look at some of the advantages and disadvantages of using Kruskal’s algorithm.

What is a Minimum Spanning Tree?

A minimum spanning tree (MST) is a subset of the edges of a connected, undirected graph that connects all the vertices together with the minimum total weighting. In other words, it is a graph that contains all the vertices of the original graph, but only some of the edges. The total weight of the MST is the sum of the weights of the edges in the MST.

How Does Kruskal’s Algorithm Work?

Kruskal’s algorithm is a greedy algorithm that finds the minimum spanning tree of a graph. It works by looking at the edges of the graph one by one and adding them to the MST if they do not create a cycle.

The algorithm starts by sorting the edges of the graph in increasing order of their weights. Then, it looks at the edges one by one and adds them to the MST if they do not create a cycle. The algorithm keeps adding edges until all the vertices are connected.

Pseudocode

The pseudocode for Kruskal’s algorithm is given below:

Kruskal(G):
    A = empty set
    for each vertex v in G.V:
        MakeSet(v)
    sort the edges of G.E in increasing order of their weights
    for each edge (u, v) in G.E:
        if FindSet(u) != FindSet(v):
            A = A U {(u, v)}
            Union(u, v)
    return A

Advantages and Disadvantages

Kruskal’s algorithm is a simple and efficient algorithm for finding the minimum spanning tree of a graph. It is also quite easy to implement and can be used to solve a variety of problems.

However, Kruskal’s algorithm is not the most efficient algorithm for finding the minimum spanning tree. It is also not suitable for graphs with negative edge weights.

Conclusion

Kruskal’s algorithm is a popular and efficient algorithm for finding the minimum spanning tree of a graph. It is a greedy algorithm that works by looking at the edges of the graph one by one and adding them to the MST if they do not create a cycle. The pseudocode for the algorithm is given above and its advantages and disadvantages are discussed.