# Lecture 24

You may want to download the lecture slides that were used for these videos (PDF).

## 1. It’s All About Augmenting Paths

Let L denote the set of all vertices X for which there is an augmenting path from S to X, and let R be the remaining vertices. Then if e is an edge from L to R, it follows that e is full. On the other hand, if f is an edge from R to L, then f is empty. (5:15)

## 2. Augmenting Paths – Be Careful

We should focus on finding augmenting paths using the minimum number of edges. (5:21)

## 3. Primal Dual with Dijstra as the Dual

Our strategy is to use Dijkstra to find an augmenting path using the minimum number of edges. Normally, this is done by carrying out the Ford-Fulkerson labelling algorithm. This algorithm assigns triples to vertices of the network, starting with a labelling of the source S. (6:53)

## 4. Primal Dual with Dijstra as the Dual

This video starts an example of the Ford-Fulerson algorithm. (14:07)

## 5. The Example Updated

This video completes our example of the Ford-Fulerson algorithm. (4:47)

## 6. A Second Example

In this video we discuss a the Ford-Fulkerson labelling algorithm on another network flow. The video that follows after this video will present the solution. (3:25)

## 7. A Second Example (Solution)

This video presents the Ford-Fulkerson labelling algorithm on the second network flow example. (9:42)

## 8. A Second Example (Discussion)

This video presents concludes our discussion of the second example. (5:09)

## 9. Network Flows and Linear Programming

Let’s connect network flows with linear programming. (4:36)

## 10. Some Observations on LP problems

This video presents some comments on LP problems. We also pose a problem that we will solve in the next lecture. (4:03)