Lec 78 - Minimum Cost Spanning Trees: Kruskal's Algorithm
IIT Madras - B.S. Degree Programme・2 minutes read
Kruskal's Algorithm and Prim's Algorithm both find minimum cost spanning trees in weighted undirected graphs but follow different strategies and sequences. Kruskal's Algorithm connects components with the smallest edge, avoiding cycles and sorting edges by weight, while Prim's Algorithm grows the tree gradually, leading to multiple possible spanning trees with repeated edge weights.
Insights
- Kruskal's Algorithm and Prim's Algorithm both find the same minimum cost spanning tree but follow distinct processes, with Kruskal's focusing on sorting edges and connecting components without cycles, while Prim's grows the tree incrementally.
- In scenarios where edge weights are repeated, multiple spanning trees with the same minimum cost could emerge due to different edge sets resulting from varying vertex ordering, showcasing the impact of seemingly minor details on the final outcome.
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Recent questions
What are the two main strategies for minimum cost spanning trees?
Prim's strategy and Kruskal's Algorithm
How does Kruskal's Algorithm avoid creating cycles?
By skipping edges that connect vertices within the same component.
What is the key principle behind Kruskal's Algorithm?
Adding the smallest edge connecting different components.
How does Kruskal's Algorithm differ from Prim's Algorithm in tree construction?
Kruskal's Algorithm assembles the tree bottom-up, while Prim's Algorithm grows the tree gradually.
How do repeated edge weights impact the construction of spanning trees?
They may lead to multiple possible spanning trees with different edge sets.
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