Discussion
Compute the maximal flow through the following network :
Answer: A
The maximal flow is 70 units.
The two arcs leaving the source, S-1 (40) and S-2 (30), form a cut of capacity 70, so no flow can exceed 70. A flow of 70 can be achieved:
- S to 1: 40, sent on as 30 to node 3, 5 to node 4 and 5 to node 2.
- S to 2: 30, plus 5 from node 1, so 35 goes on to node 4.
- Node 4 receives 5 + 35 = 40: 30 goes to N and 10 to node 3 on the undirected arc 3-4 (capacity 25).
- Node 3 receives 30 + 10 = 40 and sends it to N (capacity 50).
The flow into N is 40 + 30 = 70, equal to the cut, so by the max-flow min-cut theorem it is maximal. 75 exceeds the cut; 60 and 65 stop short of a flow that is achievable.
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