20.6. Updating W Matrices

Try these first

1. 1.

   Define the transitive closure in your own words.

   Hint

   Think of paths in a graph.

2. 2.

   Explain what Warshall's algorithm does.

   Hint

   Consider how matrices represent paths.

3. 3.

   What does Warshall's algorithm compute?

   • Minimum Spanning Tree
   • Transitive Closure
   • Shortest Path

   Hint

   Recall the primary goal of the algorithm.

4. 4.

   True or False: Warshall’s algorithm requires O(n²) time for updating each entry during matrix transformation.

   • True
   • False

   Hint

   Think about how the updates are structured.

5. 5.

   Given a directed graph with nodes 1 to 4 and edges (1, 2), (2, 3), and (3, 4), determine the transitive closure using Warshall's algorithm.

   Hint

   Visualize each step of matrix updates to track connectivity.

6. 6.

   Consider a directed graph with a cycle. How would Warshall's algorithm adapt to ensure all nodes in the cycle reflect their connectivity?

   Hint

   Identify the cycle and how its nodes interact as intermediates.