Computer Science 226
Algorithms and Data Structures
Spring 2013

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Max Flow

Things to Know Before Lecture

It's not absolutely necessary to be able to solve a Ford-Fulkerson problem by hand, but it's probably a good idea. See checklist problem #2.

Pre-Lecture Preparation Guide.

High priority videos are in red. Low priority videos are in blue.

Maxflow Basics 0m - 10m 33s
1-12, 15
Ford Fulkerson 0m - 6m 30s
891-892 16-23 Demo
Maxflow-Mincut theorem 0m - 9m 30s
892-894 24-33

Checkpoint 1: Everything in the diagram below should make sense. Specifically, you should understand:

  1. That the first number on each edge is the "edge flow", and the second number is the "edge capacity".
  2. That the vertices in blue are on the s side of the s-t cut, and the vertices in white are on the t side.
  3. That s is the source, and t is the sink.
  4. That the value of this flow is 28.
  5. That the capacity of the min-cut is 28.
  6. That there are no more augmenting paths, because all the forward edges from s-t to are full, and all the backward edges from t-s are empty.

Checkpoint 2: Optional: You should be able to solve a max flow exercise using Ford-Fulkerson. We will be going through the demo in the slides, though, so if you don't get around to it, no big deal. Recommended technique: Try to do the problem in the demo, then come back and see if your answer was right. You do NOT need to identify the same sequence of augmenting paths (unlike Prim's / Kruskal's / Dijkstra's, there is no canonical order!).