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ENGM 792 Network Flow Programming

ENGM 792 Network Flow Programming. Shortest Path Solutions. Shortest Path . (Cost ) [External Flow]. (10). 2. 7. (6). (4). (1). (40). 5. (4). (0). (20). (2). (8). (20). [1]. 1. 10. [-1]. 3. (2). 8. (2). (4). (2). 6. (12). (10). (10). (3). (1). (6). 4. 9.

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ENGM 792 Network Flow Programming

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  1. ENGM 792Network Flow Programming Shortest Path Solutions

  2. Shortest Path (Cost) [External Flow] (10) 2 7 (6) (4) (1) (40) 5 (4) (0) (20) (2) (8) (20) [1] 1 10 [-1] 3 (2) 8 (2) (4) (2) 6 (12) (10) (10) (3) (1) (6) 4 9

  3. Dijkstra’s Algorithm • Initial : let S={s}, s=0 • Find an arc k(i,j) that passes from an unsolved node to a solved node such that • Add node j and arc k(i,j) to tree • Add j to solved set S. Let j=I + ck • Go to step 2, repeat until S = set of all nodes

  4. Shortest Path (Cost) [s] (10) 2 7 (6) (4) (1) (40) 5 (4) (0) (20) (2) [8] [0] (8) (20) 1 10 3 (2) 8 (2) (4) (2) 6 (12) (10) (10) (3) (1) (6) 4 9

  5. solved closest length to node length of Iter nodes unsolved unsolved added shortest path 1 1 3 8 3 8

  6. Shortest Path (Cost) [s] (10) 2 7 (6) (4) (1) (40) 5 (4) (0) (20) (2) [8] [0] (8) (20) 1 10 3 (2) 8 (2) (4) (2) 6 (12) (10) (10) (3) (1) (6) 4 9

  7. Shortest Path (Cost) [s] (10) 2 7 (6) (4) (1) (40) 5 (4) (0) (20) (2) [8] [0] (8) (20) 1 10 3 (2) 8 (2) (4) [10] (2) 6 (12) (10) (10) (3) (1) (6) 4 9 [10]

  8. Shortest Path (Cost) [s] (10) 2 7 (6) (4) (1) (40) 5 (4) (0) (20) (2) [8] [0] (8) (20) 1 10 3 (2) 8 (2) (4) (2) 6 (12) (10) (10) (3) (1) (6) 4 9 [10]

  9. solved closest length to node length of Iter nodes unsolved unsolved added shortest path 1 1 3 8 3 8 2 1 4 10 3 6 10 4 10

  10. Shortest Path (Cost) [s] (10) 2 7 (6) (4) (1) (40) 5 (4) (0) (20) (2) [8] [0] (8) (20) 1 10 3 (2) 8 (2) (4) [10] (2) 6 (12) (10) (10) (3) (1) (6) 4 9 [10]

  11. solved closest length to node length of Iter nodes unsolved unsolved added shortest path 1 1 3 8 3 8 2 1 4 10 3 6 10 4 10 3 1 2 40 3 6 10 6 10 4 6 11

  12. Shortest Path [12] (Cost) [s] (10) 2 7 (6) (4) (1) (40) 5 (4) (0) (20) (2) [8] [0] (8) (20) 1 10 3 (2) 8 (2) (4) [10] (2) 6 (12) (10) (10) (3) (1) (6) 4 9 [10]

  13. Shortest Path [12] (Cost) [s] (10) 2 7 (6) (4) (1) 5 (4) (0) (20) [8] [0] (8) (20) 1 10 3 8 (2) (4) [10] (2) 6 (10) (10) (3) 4 9 [10]

  14. solved closest length to node length of Iter nodes unsolved unsolved added shortest path 1 1 3 8 3 8 2 1 4 10 3 6 10 4 10 3 1 2 40 3 6 10 6 10 4 6 11 4 1 2 40 3 2 12 2 12 6 9 13

  15. Shortest Path [12] (Cost) [s] (10) 2 7 (6) (4) (1) 5 (4) (0) (20) [8] [0] (8) (20) 1 10 3 8 (2) (4) [10] (2) 6 (10) (10) (3) 4 9 [10]

  16. Shortest Path [12] (Cost) [s] (10) 2 7 (6) (4) (1) 5 (4) (0) (20) [8] [0] (8) (20) 1 10 3 8 (2) (4) [10] (2) 6 (10) (10) (3) 4 9 [10] [13]

  17. solved closest length to node length of Iter nodes unsolved unsolved added shortest path 1 1 3 8 3 8 2 1 4 10 3 6 10 4 10 3 1 2 40 3 6 10 6 10 4 6 11 4 1 2 40 3 2 12 2 12 6 9 13 5 2 5 18 6 9 13 9 13

  18. Shortest Path [12] (Cost) [s] (10) 2 7 (6) (4) (1) 5 (4) (0) (20) [8] [0] (8) (20) 1 10 3 8 (2) (4) [10] (2) 6 (10) (10) (3) 4 9 [10] [13]

  19. Shortest Path [12] (Cost) [s] (10) 2 7 (6) (4) (1) 5 (4) (0) (20) [8] [0] [14] (8) (20) 1 10 3 8 (2) (4) [10] (2) 6 (10) (10) (3) 4 9 [10] [13]

  20. Shortest Path [12] (Cost) [s] (10) 2 7 (6) (4) (1) 5 (4) (0) [8] [0] [14] (8) (20) 1 10 3 8 (2) (4) [10] (2) 6 (10) (3) 4 9 [10] [13]

  21. solved closest length to node length of Iter nodes unsolved unsolved added shortest path 1 1 3 8 3 8 2 1 4 10 3 6 10 4 10 3 1 2 40 3 6 10 6 10 4 6 11 4 1 2 40 3 2 12 2 12 6 9 13 5 2 5 18 6 9 13 9 13 6 2 5 18 6 8 14 6 14 9 10 15

  22. Shortest Path [12] (Cost) [s] (10) 2 7 (6) (4) (1) 5 (4) (0) [8] [0] [14] (8) (20) 1 10 3 8 (2) (4) [10] (2) 6 (10) (3) 4 9 [10] [13]

  23. Shortest Path [12] (Cost) [s] (10) 2 7 (6) [14] (4) (1) 5 (4) (0) [8] [0] [14] (8) (20) 1 10 3 8 (2) (4) [10] (2) 6 (10) (3) 4 9 [10] [13]

  24. Shortest Path [12] (Cost) [s] (10) 2 7 [14] (4) (1) 5 (4) (0) [14] [8] [0] (8) (20) 1 10 3 8 (2) (4) [10] (2) 6 (10) (3) 4 9 [10] [13]

  25. solved closest length to node length of Iter nodes unsolved unsolved added shortest path 4 1 2 40 3 2 12 2 12 6 9 13 5 2 5 18 6 9 13 9 13 6 2 5 18 6 8 14 6 14 9 10 15 7 2 7 22 8 5 14 5 14 9 10 15

  26. Shortest Path [12] (Cost) [s] (10) 2 7 [14] (4) (1) 5 (4) (0) [14] [8] [0] (8) (20) 1 10 3 8 (2) (4) [10] (2) 6 (10) (3) 4 9 [10] [13]

  27. Shortest Path [12] (Cost) [s] (10) 2 7 [14] (4) (1) 5 (4) (0) [14] [8] [0] (8) (20) 1 10 [15] 3 8 (2) (4) [10] (2) 6 (10) (3) 4 9 [10] [13]

  28. Shortest Path [12] (Cost) [s] (10) 2 7 [14] (4) 5 (4) (0) [14] [8] [0] (8) 1 10 [15] 3 8 (2) (4) [10] (2) 6 (10) (3) 4 9 [10] [13]

  29. solved closest length to node length of Iter nodes unsolved unsolved added shortest path 5 2 5 18 6 9 13 9 13 6 2 5 18 6 8 14 6 14 9 10 15 7 2 7 22 8 5 14 5 14 9 10 15 8 2 7 22 5 7 18 8 10 24 9 10 15 10 15

  30. Shortest Path [12] (Cost) [s] (10) [18] 2 7 [14] (4) 5 (4) (0) [14] [8] [0] (8) 1 10 [15] 3 8 (2) (4) [10] (2) 6 (10) (3) 4 9 [10] [13]

  31. Shortest Path [12] (Cost) [s] [18] 2 7 [14] (4) 5 (4) (0) [14] [8] [0] (8) 1 10 [15] 3 8 (2) (4) [10] (2) 6 (10) (3) 4 9 [10] [13]

  32. solved closest length to node length of Iter nodes unsolved unsolved added shortest path 5 2 5 18 6 9 13 9 13 6 2 5 18 6 8 14 6 14 9 10 15 7 2 7 22 8 5 14 5 14 9 10 15 8 2 7 22 5 7 18 8 10 24 9 10 15 10 15 9 2 7 22 5 7 18 7 18

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