Lecture 27

Learning objectives

After this class, you should be able to:

1. Explain the meaning of the following terms: residual network, residual capacity, augmenting path, cut, net flow across a cut, capacity of a cut, and a minimum cut.
2. Prove the max-flow min-cut theorem.
3. Given a flow network and a flow, find an augmenting path, and determine a flow with a greater value.
4. Given a network flow, apply the Edmonds-Karp algorithm to find a max-flow.
5. Prove that the time complexity of the Edmonds-Karp algorithm is O(VE²).

Reading assignment

1. CLR: Section 26.2.
2. None -- prepare for final exam!

Exercises and review questions

• Questions on current lecture's material
  1. In the previous lecture's review questions, you determined an augmenting path for a network flow example. Determine the new flow that results from using this augmenting path to increase the flow.
  2. Find a maximum flow for the network flow example you created for the previous lectures. Give a min-cut corresponding to this max-flow.
  3. CLR: Exercise 26.2-7.
  4. CLR: Exercise 26.2-2. (Please bring a hardcopy of your solution to class.)
  5. CLR: Exercise 26.2-10.
• Questions on next lecture's material
  1. None.