7. Dinic Algorithm
Learn about the Dinic Algorithm — its flow values, capacities, and residual capacities using a flow network instance. Explore the algorithm's application in network flow optimization.
7. Dinic Algorithm
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Presentation Transcript
Max-Flow instance 0 flow 2 4 4 capacity G: 0 0 0 6 0 8 10 10 2 0 0 0 0 10 s 3 5 t 10 9 Flow value = 0 2
0 0 Dinic Algorithm Flow value = 0 0 flow 2 4 4 capacity G: 0 0 6 0 8 10 10 2 0 0 0 10 s 3 5 t 10 9 2 4 4 residual capacity Gf: 6 8 10 10 2 10 s 3 5 t 10 9 2 4 4 4 5 GL: 4 1 X 8 10 10 1 10 s 3 5 t 10 9 9 10 9 X 9 3
0 0 Dinic Algorithm Flow value = 14 0 4 X 2 4 4 G: 4 X 0 X X 0 5 1 6 0 8 10 10 2 0 9 10 9 X 0 0 X X 10 s 3 5 t 10 9 2 4 4 4 Gf: 5 1 6 7 6 5 2 1 s 3 5 t 10 9 9 2 4 GL: 5 5 5 6 7 6 5 5 1 s 3 5 t 4
5 0 Dinic Algorithm Flow value = 19 0 4 X 2 4 4 G: 9 4 X X 1 10 X 6 X 6 0 8 10 10 2 0 5 9 10 9 X 0 0 X X 10 s 3 5 t 10 9 2 4 4 9 Gf: 6 1 2 1 10 2 5 1 s 3 5 t 10 9 9 2 4 GL: 1 2 1 1 s 3 5 t 5
5 0 Dinic Algorithm 0 4 X 2 4 4 G: 9 4 X X 10 1 X 6 X 6 0 8 10 10 2 0 5 9 10 9 X 0 0 X X 10 s 3 5 t 10 9 Cut capacity = 19 Flow value = 19 2 4 4 9 Gf: 6 1 2 1 10 2 5 1 s 5 t 10 9 3 9 6
