"Strip mining" is the same as "open pit mining." This is a method of retrieving metal and other precious resources from under ground.
The instructor will spend the whole lecture on this problem reduction. He wants to show all of the details so that the students can see the whole process, since these details can be tricky.
The instructor makes the point that today we will be working with cuts, not flows. He then reviews the definition of a cut.
Explaining the Open Pit Mining problem.
Herre the instructor formulates the Open Pit Mining problem as a graph.
At 8:29, he asks, "What is the total value associated with this mine?" A student responds, "-6" You should stop here to let the students respond.
The problem statement can be summarized by the following: Maximize the profit subject to the rule that if we want to remove a node, we must remove all of its predecessors in the graph.
This is an activity slide. You can stop the video at 9:45.
At 16:40, the instructor asks, "How did you solve this problem?" The student response is hard to hear, but the instructor summarizes: "Guess and verify."
The instructor begins discussing how a cut applies to this problem.
A precedence graph is a directed acyclic graph.
At 18:45, the instructor asks, "What is a feasible set containing 5?" A student responds, "5, -3, -4, -2" You should stop here to let students respond.
The instructor states that the feasible sets are exactly the open pit mines that follow the rule stated earlier.
To construct the graph, we assign infinite capacity to each edge. Then we add a source s and a sink t. Then for each vertex v in the graph, we add finite capacity edges from s to v and from v to t. We will then look for a minimum cut. Since we can't use any of the infinite edges in the cut, this ensures that we will end up with a feasible set.
This is an acivity slide. You can stop the video at 22:50.
At 24:10, the instructor clarifies the definition of an s-t cut: a partition of the vertices with s on one side and t on the other.
The instructor displays an incorrect solution before showing several correct solutions.
The instructor makes the point that infinite edges from the t side to the s side are ok, but we are not allowed to have any infinite edges from the s side to the t side.
At 29:45, he states the above point: "We need to look at all of the black edges crossing the cut. They all need to go from the t side to the s side."
The vertices on the t side of the cut will be our feasible set.
Here we assign values to the finite-cost edges in our graph.
At 36:45, the instructor is gesturing to the red edges (you can't see this in the video).
This is an activity slide. You can stop the video at 37:12.
"Enumerate" means "list".
At 37:27, a student asks, "Do we need to put two nodes on each side of the cut (like the last activity)?" The instructor responds, "No."
There were a total of 6 possible cuts.
At 43:11, the instructor asks, "Were we just lucky that the min cut corresponded to the best feasible set?" He gets no response, but stop here to let students respond (or ask them this question yourself.)
At 43:43, the instructor asks, "How does the value of the min cut relate to the value of the best feasible set?" The student response is hard to hear, but the instructor repeats it, and writes it down. If you didn't get the desired response from the previous question, stop again.
The red edges of the cut correspond to the cost of the cut, and the blue edges correspond to the benefit not received.
This is an activity slide. You can stop the video at 46:40.
This was not done as an activity in the UW class; the instructor just did it quickly. If the students have a difficult time with the activity it might be worthwhile to show this discussion.
At 47:55, the instructor asks, "What's Ben(S) + Ben(T)" This is B.
So Cap(S, T) = B - Profit(T). Since B is a constant, maximizing Profit(T) corresponds to minimizing Cap(S, T), or the min cut.
The instructor makes the point that he showed all of the details today because the details of these constructions can be complicated, and it can be hard to get all of the details right. Since the students have to do it on homework, he wanted to show all of the details for one construction.