20.7. Summary of Update Processes

Try these first

1. 1.

   What does the initial matrix W⁰ represent?

   Hint

   Think about how connections in a graph are shown.

2. 2.

   What is the time complexity of Warshall's Algorithm?

   Hint

   How does this compare to the naive approach?

3. 3.

   What operation is used to compute connectivity in Warshall's Algorithm?

   • Addition
   • Boolean Operations
   • Matrix Multiplication

   Hint

   Think about the type of entries present in the matrix.

4. 4.

   True or False: Warshall's Algorithm can be used to find all paths between nodes in a directed graph.

   • True
   • False

   Hint

   What does the term transitive suggest about the paths?

5. 5.

   Given a directed graph with nodes A, B, C, and direct connections A to B and B to C, compute the transitive closure step-by-step.

   Hint

   Remember to consider all paths through any intermediate nodes at each step.

6. 6.

   What would happen to the connectivity matrix if a new direct edge is added from node C to node A?

   Hint

   Consider directly how this changes the paths available.