3.4. Minimum Separator Lemma

Try these first

1. 1.

   What is a spanning tree in the context of a graph?

   Hint

   Think about the properties of trees.

2. 2.

   What is a greedy algorithm?

   Hint

   Consider how you would make decisions based on current options.

3. 3.

   What is the main goal of Prim's algorithm?

   • To find the shortest path
   • To find the minimum cost spanning tree
   • To find all paths

   Hint

   Consider the definition of a spanning tree.

4. 4.

   True or False: Prim's algorithm can work with disconnected graphs.

   • True
   • False

   Hint

   Think about the requirements for forming a spanning tree.

5. 5.

   Given a graph with vertices A, B, C, D, and edges AB=1, AC=2, AD=3, BC=3, BD=2, CD=1, apply Prim's algorithm to find the minimum spanning tree.

   Hint

   List your edges by weight and think about how to connect new vertices at each step.

6. 6.

   Consider a scenario where a graph has multiple edges between vertices with the same minimum weight. Discuss how Prim's algorithm handles this situation.

   Hint

   Think about how the algorithm can choose edges that share the same weight.