7. Dinic Algorithm 5/15/2019 Copyright 2000, Kevin Wayne

Max-Flow instance G: flow capacity Flow value = 0 2 4 s 3 5 t 5/15/2019 Max-Flow instance flow 2 4 4 capacity G: 10 8 6 2 10 s 10 3 9 5 10 t Flow value = 0 Copyright 2000, Kevin Wayne 2

Dinic Algorithm G: Gf: GL: Flow value = 0 flow capacity 5/15/2019 Dinic Algorithm Flow value = 0 flow 2 4 4 capacity G: 10 8 6 2 10 s 10 3 9 5 10 t 2 4 4 residual capacity Gf: 10 8 6 2 10 s 10 3 9 5 10 t 2 4 4 5 4 GL: 1 4 X 10 8 10 1 s 10 3 9 5 10 t 9 9 9 X 10 Copyright 2000, Kevin Wayne 3

Dinic Algorithm G: Gf: GL: Flow value = 14 X X X X X X X 5 5 5 5 5 5 5 5/15/2019 Dinic Algorithm Flow value = 14 X 4 2 4 4 G: X X 4 5 X 1 10 8 6 2 10 9 9 10 X X X s 10 3 9 5 10 t 2 4 4 Gf: 4 5 1 5 7 6 2 6 s 1 3 9 5 10 t 9 2 4 GL: 5 5 5 5 7 6 6 5 s 1 3 5 t Copyright 2000, Kevin Wayne 4

Dinic Algorithm G: Gf: GL: Flow value = 19 X X 5 1 X 4 X X X X X 10 2 5/15/2019 Dinic Algorithm Flow value = 19 X 4 2 4 4 G: X 9 10 5 1 X 6 4 X 10 8 6 X 2 10 5 9 10 X 9 X X s 10 3 9 5 10 t 2 4 4 Gf: 9 6 10 2 1 2 1 5 s 1 3 9 5 10 t 9 2 4 GL: 2 1 1 s 1 3 5 t Copyright 2000, Kevin Wayne 5

Dinic Algorithm G: Gf: X X 5 4 X 1 X X X X X Cut capacity = 19 5/15/2019 Dinic Algorithm X 4 2 4 4 G: X 5 4 X 9 10 1 X 6 8 6 X 10 2 10 5 9 9 10 X X X s 10 3 9 5 10 t Cut capacity = 19 Flow value = 19 2 4 4 Gf: 9 6 10 2 1 2 1 5 s 1 3 9 5 10 t 9 Copyright 2000, Kevin Wayne 6