Graph theory (AIHL 3.15, 3.16) - Part 3 Minimum Spanning Trees
Inquiry questions
| Factual Questions: What defines a Minimum Spanning Tree (MST) in graph theory? How does Kruskal's algorithm find the MST in a graph? Describe the process of Prim's algorithm for generating an MST. | Conceptual Questions: Compare and contrast Kruskal’s and Prim’s algorithms in terms of their approach to finding an MST. What role does the concept of "minimum total edge weight" play in the definition and finding of an MST? How do the implementations of Kruskal's and Prim's algorithms differ when using an adjacency matrix? | Debatable Questions: Which algorithm, Kruskal's or Prim's, is generally more efficient in practice for finding an MST, considering various graph structures? Can the choice between using Kruskal’s and Prim’s algorithms significantly affect the performance of network design and optimization tasks? In the context of real-world applications, how critical is the distinction between choosing Kruskal’s versus Prim’s algorithm for constructing minimum spanning trees? |
Minimum Spanning Tree (MST) Graph Algorithms: These algorithms find a subset of the edges of a connected, undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight.
Kruskal’s and Prim’s Algorithms: These are two different algorithms for finding the MST of a graph. Kruskal’s algorithm adds the shortest edge that doesn’t produce a cycle until all vertices are connected, while Prim’s algorithm grows the MST one vertex at a time, always choosing the cheapest edge to add.
Exploring Kruskals algorithm
Explain Kruskal's algorithm in your own words
Exploring Prim's algorithm
Explain Prim's algorithm in your own words
