7 FordFulkerson Algorithm with multiple optimal solutions Algorithm

7. Ford-Fulkerson Algorithm with multiple optimal solutions Algorithm Design by Éva Tardos and Jon Kleinberg • Copyright © 2005 Addison Wesley • Slides by Kevin Wayne

Ford-Fulkerson Algorithm flow G: 0 1 s 0 4 2 0 1 0 3 1 4 0 0 1 1 5 capacity 0 4 t Flow value = 0 2

Ford-Fulkerson Algorithm flow G: 0 1 0 s 4 3 1 0 1 1 5 2 4 t Flow value = 0 4 1 1 0 3 capacity 4 0 1 s 0 1 0 Gf: 4 2 5 4 t 1 3

Ford-Fulkerson Algorithm flow G: 1 1 s 1 4 3 1 0 1 1 5 1 2 4 t Flow value = 1 4 1 1 0 3 capacity 4 0 1 3 1 1 0 Gf: s 2 5 1 3 t 1 4

Ford-Fulkerson Algorithm flow G: 1 1 s 2 4 2 1 1 2 0 3 1 1 1 5 Gf: 1 capacity 4 1 1 2 s 2 3 4 1 1 t Flow value = 2 1 2 4 5 2 2 t 1 5

Ford-Fulkerson Algorithm flow G: 1 1 s 2 4 2 1 1 1 3 4 1 1 1 Gf: 1 capacity 5 2 2 t 1 3 4 1 1 4 Flow value = 3 1 s 2 5 2 1 t 1 6

Ford-Fulkerson Algorithm flow G: 1 1 s 2 3 2 1 1 1 3 1 4 1 1 Gf: 1 5 capacity 2 2 t 1 4 3 1 3 Flow value = 3 1 s 2 5 2 1 t 1 7

Ford-Fulkerson Algorithm flow G: 1 1 s 2 3 2 1 1 1 3 1 4 1 1 Gf: 1 5 capacity 2 2 t 1 4 3 1 3 Flow value = 3 1 s 2 5 2 1 t 1 8

Ford-Fulkerson Algorithm flow G: 1 1 s 2 3 2 1 1 1 3 1 4 1 1 Gf: 1 5 capacity 2 2 t 1 4 3 1 3 Flow value = 3 1 s 2 5 2 1 t 1 9

Ford-Fulkerson Algorithm flow G: 1 1 s 2 3 2 1 1 1 3 1 4 1 1 Gf: 1 5 capacity 2 2 t 1 4 3 1 3 Flow value = 3 1 s 2 5 2 1 t 1 10