Network Flow I: Max-cut min-flow theorem, augmenting paths, Ford-Fulkerson

Slides:

https://www2.compute.dtu.dk/courses/02110/2023/slides/flow1-1x1.pdf

Problems:

https://www2.compute.dtu.dk/courses/02110/2023/weekplans/network1.pdf

Reading

• KT 7.1, Page 338

• KT 7.2, Page 346

Videos

Ford-Fulkerson in 5 minutes

Max Flow Ford Fulkerson | Network Flow | Graph Theory

Key terms: Backward edge. Going in to opposite direction (undo a flow)

If the forward paths are full and the backward path are empty the algorithm is done.

You can choose different paths but should end up with the same flow value

If you code the algorithm you will likely use DFS at each iteration to find the path

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Time Comlexity: O(E·f)

E = # of edges

f = maximum flow

What is max flow and minimum cut: Smallest capacity cut, ST-cut,

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Max flow = min cut = 4

Edmonds Karp Algorithm

Edmonds Karp Algorithm | Network Flow | Graph Theory

BFS instead of DFS, because of time complexity

Network Flows I

Lecture