10.3. Special Graph Type

Try these first

1. 1.

   What is the principle of flow conservation?

   Hint

   Think about a water tank where the water coming in and going out must be balanced.

2. 2.

   Name the algorithm used to calculate the maximum flow.

   Hint

   Remember the term associated with 'finding paths with spare capacity.'

3. 3.

   What principle states that the inflow and outflow of nodes must balance?

   • Augmentation
   • Flow Conservation
   • Max-flow

   Hint

   Consider the water flow metaphor again!

4. 4.

   True or False: The Ford-Fulkerson algorithm can provide an optimal solution to network flow problems.

   • True
   • False

   Hint

   Think about its iterative nature to improve flow.

5. 5.

   Challenge: Given a graph with nodes and edge capacities, use the Ford-Fulkerson algorithm to solve for maximum flow. List your steps and the resulting flows.

   Hint

   Make sure to visualize every step and track any adjustments made to capacities.

6. 6.

   Challenge: Create a scenario with a minimum cut that restricts the flow to a specific maximum. What's the relationship between the identified cut and flow?

   Hint

   Draw the cut and identify which edges limit maximum flow.