3.6. Final Algorithm for Prim's Minimum Cost Spanning Tree

Try these first

1. 1.

   Define Prim's algorithm in your own words.

   Hint

   Focus on the steps and how it builds the tree.

2. 2.

   What does a spanning tree do?

   Hint

   Think about what a tree structure is.

3. 3.

   What does Prim's algorithm find in a graph?

   • Longest path
   • Minimum spanning tree
   • Largest cycle

   Hint

   Recall the objective of the algorithm.

4. 4.

   True or False: Prim's algorithm can only be used on directed graphs.

   • True
   • False

   Hint

   Think about the nature of the graph used.

5. 5.

   Given a graph with several vertices and edges of varying weights, demonstrate Prim's algorithm step-by-step, explaining each decision made along the way.

   Hint

   Track your choices to validate each step against the minimum separator lemma.

6. 6.

   Construct a comprehensive analysis of comparing Prim's and Kruskal's algorithms when applied to a dense versus a sparse graph. Discuss efficiency and outcomes for both.

   Hint

   Review their operating principles and how those relate to graph characteristics.