Lecture 26

Learning objectives

After this class, you should be able to:

1. Define a flow network, the conditions a flow should satisfy, and the maximum flow problem.
2. Transform a problem that does not exactly satisfy the requirements of the network flow problem, into one that does.
3. Given an expression using the implicit summation notation, show an equivalent expression that explicitly shows the summations, and vice versa.
4. Prove properties of network flows, such as those in Lemma 26.1.

Reading assignment

1. CLR: Chapter 26, up to (and including) sec 26.1.
2. CLR: Section 26.2, page 651-652, 655.

Exercises and review questions

• Questions on current lecture's material
  1. CLR: Exercise 26.1-1.
  2. CLR: Exercise 26.1-4.
  3. CLR: Exercise 26.1-6.
• Questions on next lecture's material
  1. (Submit a hardcopy) Show the residual network and an augmenting path for the network flow example you created for the previous lecture's review questions.
  2. (Submit a hardcopy) Give a cut, and the net flow and capacity across that cut, for the network flow example you created for the previous lecture's review questions.