Difference between Prim’s and Kruskal’s algorithm for MST
Prim's and Kruskal's techniques target a graph's minimal spanning tree. These algorithms handle the same issue in various ways. Prim's Technique is a greedy algorithm to locate the smallest spanning tree in a graph. On the other hand, Kruskal's Algorithm is used to locate the lowest spanning tree for a linked weighted graph. The primary objective of the method is to identify the subset of edges required to visit each vertex of the graph.
Following a quick introduction to Prim's and Kruskal's algorithm, we will examine the whole list and the difference between Prim's and Kruskal's Algorithm. Let's examine the differences between Prim's and Kruskal's Algorithm in detail.
What is Prim's Algorithm?
Additionally, Prim's algorithm is a Greedy algorithm. It begins with a spanning tree that is empty. The objective is to preserve two sets of vertices. The first set comprises the vertices that have already been included in the MST, while the second set contains the vertices that have not yet been included. At each step, it evaluates all edges connecting the two sets and selects the edge with the lowest weight. After selecting the edge, it adds the opposite endpoint to the set containing MST.
Advantages:
- The Prim method helps deal with dense networks with many edges.
- It is more sophisticated than Kruskal's algorithm.
Disadvantages:
- When numerous edges have the same weight, Prim's algorithm does not provide much control over the selected edges. This is because just the detected edges are put in the queue, as opposed to all edges, as in Kruskal's method.
What is Kruskal's Algorithm?
Given a connected and undirected graph, a spanning tree of that graph is a tree-shaped subgraph that links all vertices. A single graph may have several spanning trees. A minimal spanning tree (MST) or minimum weight spanning tree is a spanning tree with a weight less than or equal to the weight of every other spanning tree in a weighted, linked, undirected graph. The weight of a spanning tree is the total of the weights assigned to each of its edges.
Advantages:
- Kruskal performs better in normal circumstances (sparse graphs) and is simpler to construct due to its usage of disjoint sets and more superficial data structure s.
Disadvantages:
- If the number of nodes is vast, the Kruskal method will be sluggish, since it must first sort thousands of vertices before forming a route.
Prim's Algorithm vs. Kruskal's Algorithm
| Prim's Algorithm |
Kruskal's Algorithm |
- It starts to build the Minimum Spanning Tree from any vertex in the graph.
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- It starts to build the Minimum Spanning Tree from the vertex carrying minimum weight in the graph.
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- It traverses one node more than one time to get the minimum distance.
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- It traverses one node only once.
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- Prim’s algorithm has a time complexity of O(V2), V being the number of vertices and can be improved up to O(E log V) using Fibonacci heaps.
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- Kruskal’s algorithm’s time complexity is O(E log V), V being the number of vertices.
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- Prim’s algorithm gives connected component as well as it works only on connected graph.
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- Kruskal’s algorithm can generate forest(disconnected components) at any instant as well as it can work on disconnected components
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- Prim’s algorithm runs faster in dense graphs.
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- Kruskal’s algorithm runs faster in sparse graphs.
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- It generates the minimum spanning tree starting from the root vertex.
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- It generates the minimum spanning tree starting from the least weighted edge.
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- Applications of prim’s algorithm are Travelling Salesman Problem, Network for roads and Rail tracks connecting all the cities etc.
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- Applications of Kruskal algorithm are LAN connection, TV Network etc.
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Conclusion
In conclusion, Prim's and Kruskal's algorithm aid in finding a graph's minimal spanning tree. The Prims method creates a minimal spanning tree beginning at the root vertex, while the Krushal algorithm generates a minimum spanning tree beginning at the edge with the least weight.
We hope you like this guide. We have begun with a quick overview of Prim's and Kruskal's algorithm. Furthermore, we also compared the benefits and drawbacks of Prim's vs. Kruskal's algorithm.
Related Questions
1. Which is faster Prim or Kruskal?
Prim's approach calculates the least spanning tree for dense networks quicker than Kruskal's technique because it just visits the nearby nodes for each node and does not need to sort the edges.
2. Is Kruskal algorithm shortest path?
Kruskal's algorithm is the notion presented in discrete mathematics' graph theory. It is used to determine the shortest route between two locations in a weighted linked graph.
3. Is Prim's algorithm greedy or dynamic?
Prim's method (also known as Jarnk's algorithm) is a greedy technique in computer science that locates the smallest spanning tree for a weighted undirected graph.
4. Is kruskal greedy?
It is a greedy method in graph theory because, at each step, it adds to the least spanning forest the next lowest-weight edge that will not create a cycle.
