10.2. Flow Properties

Try these first

1. 1.

   What is the primary goal of the Ford-Fulkerson Algorithm?

   Hint

   Think about what we want to achieve in a network.

2. 2.

   Define conservation of flow.

   Hint

   Consider flow at junctions.

3. 3.

   What does the Ford-Fulkerson Algorithm achieve?

   • Maximizes flow
   • Reduces capacity
   • Finds minimum cut

   Hint

   Think about its goal in network flow problems.

4. 4.

   True or False: The flow entering a node must equal the flow exiting that node.

   • True
   • False

   Hint

   Consider how flow interacts at junctions.

5. 5.

   Given a directed network with vertices and edges having different capacities, outline a method using the Ford-Fulkerson Algorithm to determine the maximum flow. Provide an example.

   Hint

   Think carefully about how augmenting paths interact with initial flows.

6. 6.

   Consider a hypothetical scenario where you need to optimize the flow of products from multiple sources to various sinks. Explain how the principles of maximum flow apply and strategies you might employ.

   Hint

   Evaluate the implications of source-sink connections.