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.

Reading assignment

1. CLR: Section 26.2, up to (and including) theorem 26.7.
2. Review breadth-first-search (CLR: page 531-539).

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.
• Questions on next lecture's material
  1. Show that breadth-first-search can be performed in time O(E+V) for a graph G = (V,E).
  2. Show a breadth-first tree for the network in figure 26.5.