This lecture is the main lecture introducing network flow. A short introduction was given in the previous lecture - but this lecture was designed as a self contained introduction. The goal in the lecture was to give students a chance to work with flow graphs to make the concepts more complete. The lecture was designed with five activities. My expectation, before the lecture, was that about 90 minutes of material was prepared. The plan going into the lecture was to give the material at a standard pace, and then continue the lecture during the next lecture session, again with student submissions. (The once a week Tablet model has led me to rush through submissions - since if they were not done in class, they would be discarded.)
An initial analysis of student submissions was started before class took place!
Class went generally as expected - I only had time for the first three examples - so Monday's lecture will also be with the Tablet PCs. Attendance was somewhat light - although particpation from the students present seemed good.
Activity Goals: Determine if students understand the basic problem of network flow, and then gain experience with a non-trivial example. The example has a maximum flow of 65 so the edges going out of the source are not saturated. It is possible that some students may notice there is a cut of size 65.
Planned Use: First, verify that students understand the problem. Then try to show a few solutions, and work out a correct solution (from a cheat sheet slide after the example).
Actual use: This went very much as planned, students worked on this for quite a while. I asked the class during the activity what values they had on the flow - and stopped when a large number of students reported the right answer. It was exceptionally hard to talk about the solutions - even the ones that appeared correct.
Evaluation of activity: I thought the activity was very successful, in engaging students, and in having them work a non-trivial example. All students seemed to understand the what the problem is, and this excersize did lead in to the minimum cut. When I asked why 65 was the maximum flow, a student answers by identifying a minimum cut.
Activity Goals: Determine if students understand the augmenting path concept. Two separate paths must be found, so both understanding of forward edges and backward edges is tested
Planned Use: Show a correct solution, or if there were consistent misconceptions, show and discuss the misconceptions.
Actual use:Students generally did well - it seemed like about 3/4's of the students had the right idea, so I talked about a single correct solution (chosen for artistic merit) and then put up a few other correct ones.
Evaluation of activity: This seemed effective both for assessment and reinforement.
Activity Goals: This is a mechanical assessment to verify that the residual graph definition is clear. The thing I want to ensure is that students understand the reverse edges
Planned Use: Show a correct solution.
Actual use: This was a very mechanical exercise - but did allow a few students to clarify the concept. The success rate was very high on this exercise. A couple of solutions were shown, with one talked about quickly, in detail.
Evaluation of activity: This activity was quite fast - so it worked well - if it had been much longer, it would have been busy work. I had left space expecting students to draw a new graph - and was surprised to see several in place solutions. Better instructions (or vertices to use) would have helped.
