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Find shortest path from s to t.

Dijkstra's Shortest Path Algorithm (from “Algorithm Design” by J.Kleinberg and E.Tardos). Find shortest path from s to t. 2. 24. 3. 9. s. 18. 14. 6. 2. 6. 4. 19. 30. 11. 5. 15. 5. 6. 16. 20. t. 7. 44. Dijkstra's Shortest Path Algorithm. S = { }

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Find shortest path from s to t.

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  1. Dijkstra's Shortest Path Algorithm (from “Algorithm Design” by J.Kleinberg and E.Tardos) • Find shortest path from s to t. 2 24 3 9 s 18 14 6 2 6 4 19 30 11 5 15 5 6 16 20 t 7 44

  2. Dijkstra's Shortest Path Algorithm S = { } PQ = { s, 2, 3, 4, 5, 6, 7, t }   2 24 3 0 9 s 18  14 6 2 6  4  19 30 11 5 15 5 6 16 20 t 7 44  distance label 

  3. Dijkstra's Shortest Path Algorithm S = { } PQ = { s, 2, 3, 4, 5, 6, 7, t } delmin   2 24 3 0 9 s 18  14 6 2 6  4  19 30 11 5 15 5 6 16 20 t 7 44  distance label 

  4. Dijkstra's Shortest Path Algorithm S = { s } PQ = { 2, 3, 4, 5, 6, 7, t } decrease key   9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  4  19 30 11 5 15 5 6 16 20 t 7 44  distance label  15 X

  5. Dijkstra's Shortest Path Algorithm S = { s } PQ = { 2, 3, 4, 5, 6, 7, t } delmin   9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  4  19 30 11 5 15 5 6 16 20 t 7 44  distance label  15 X

  6. Dijkstra's Shortest Path Algorithm S = { s, 2 } PQ = { 3, 4, 5, 6, 7, t }   9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  4  19 30 11 5 15 5 6 16 20 t 7 44   15 X

  7. Dijkstra's Shortest Path Algorithm S = { s, 2 } PQ = { 3, 4, 5, 6, 7, t } decrease key  33 X  9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  4  19 30 11 5 15 5 6 16 20 t 7 44   15 X

  8. Dijkstra's Shortest Path Algorithm S = { s, 2 } PQ = { 3, 4, 5, 6, 7, t }  33 X  9 X 2 24 3 0 9 delmin s 18  14 X 14 6 2 6  4  19 30 11 5 15 5 6 16 20 t 7 44   15 X

  9. Dijkstra's Shortest Path Algorithm S = { s, 2, 6 } PQ = { 3, 4, 5, 7, t } 32  33 X X  9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  44 4  X 19 30 11 5 15 5 6 16 20 t 7 44   15 X

  10. Dijkstra's Shortest Path Algorithm S = { s, 2, 6 } PQ = { 3, 4, 5, 7, t } 32  33 X X  9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  44 4  X 19 30 11 5 15 5 6 16 20 t 7 44  delmin  15 X

  11. Dijkstra's Shortest Path Algorithm S = { s, 2, 6, 7 } PQ = { 3, 4, 5, t } 32  33 X X  9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  35 44 X 4  X 19 30 11 5 15 5 6 16 20 t 7 44  59 X  15 X

  12. Dijkstra's Shortest Path Algorithm S = { s, 2, 6, 7 } PQ = { 3, 4, 5, t } delmin 32  33 X X  9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  35 44 X 4  X 19 30 11 5 15 5 6 16 20 t 7 44  59 X  15 X

  13. Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 6, 7 } PQ = { 4, 5, t } 32  33 X X  9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  35 34 44 X X 4  X 19 30 11 5 15 5 6 16 20 t 7 44  51 59 X X  15 X

  14. Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 6, 7 } PQ = { 4, 5, t } 32  33 X X  9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  35 34 44 X X 4  X 19 30 11 5 15 5 6 16 delmin 20 t 7 44  51 59 X X  15 X

  15. Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 5, 6, 7 } PQ = { 4, t } 32  33 X X  9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  45 35 34 X 44 X X 4  X 19 30 11 5 15 5 6 16 20 t 7 44  50 51 59 X X X  15 X

  16. Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 5, 6, 7 } PQ = { 4, t } 32  33 X X  9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  45 35 34 X 44 X X 4  X 19 30 11 5 delmin 15 5 6 16 20 t 7 44  50 51 59 X X X  15 X

  17. Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 4, 5, 6, 7 } PQ = { t } 32  33 X X  9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  45 35 34 X 44 X X 4  X 19 30 11 5 15 5 6 16 20 t 7 44  50 51 59 X X X  15 X

  18. Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 4, 5, 6, 7 } PQ = { t } 32  33 X X  9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  45 35 34 X 44 X X 4  X 19 30 11 5 15 5 6 16 20 t 7 44  delmin 50 51 59 X X X  15 X

  19. Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 4, 5, 6, 7, t } PQ = { } 32  33 X X  9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  45 35 34 X 44 X X 4  X 19 30 11 5 15 5 6 16 20 t 7 44  50 51 59 X X X  15 X

  20. Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 4, 5, 6, 7, t } PQ = { } 32  33 X X  9 X 2 24 3 0 9 s 18  14 X 14 6 2 6  45 35 34 X 44 X X 4  X 19 30 11 5 15 5 6 16 20 t 7 44  50 51 59 X X X  15 X

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