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15.082 and 6.855J

15.082 and 6.855J. Spanning Tree Algorithms. 10. 8. 2. 4. 6. 35. 15. 1. 25. 20. 30. 17. 21. 40. 3. 5. 7. 15. 11. The Greedy Algorithm in Action. 4. 2. 6. 1. 5. 3. 7. The Greedy Algorithm in Action. 10. 10. 8. 8. 2. 4. 6. 4. 2. 6. 35. 35. 15. 15. 1. 1.

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15.082 and 6.855J

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  1. 15.082 and 6.855J Spanning Tree Algorithms

  2. 10 8 2 4 6 35 15 1 25 20 30 17 21 40 3 5 7 15 11 The Greedy Algorithm in Action 4 2 6 1 5 3 7

  3. The Greedy Algorithm in Action 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 5 7 5 3 7 15 15 11

  4. The Greedy Algorithm in Action 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 5 7 5 3 7 15 15 11

  5. The Greedy Algorithm in Action 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 5 7 5 3 7 15 15 11

  6. The Greedy Algorithm in Action 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 5 7 5 3 7 15 15 11

  7. The Greedy Algorithm in Action 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 5 7 5 3 7 15 15 11

  8. The Greedy Algorithm in Action 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 5 7 5 3 7 15 15 11

  9. The Greedy Algorithm in Action 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 5 7 5 3 7 15 15 11

  10. The Greedy Algorithm in Action 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 5 7 5 3 7 15 15 11

  11. The Greedy Algorithm in Action 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 5 7 5 3 7 15 15 11

  12. The Greedy Algorithm in Action 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 5 7 5 3 7 15 15 11

  13. The Greedy Algorithm in Action 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 5 7 5 3 7 15 15 11

  14. The Greedy Algorithm in Action 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 5 7 5 3 7 15 15 11

  15. root node The Greedy Algorithm in Action Node 1 2 3 4 5 6 7 First 1 2 3 4 5 4 7 10 10 8 8 2 4 6 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 5 7 5 3 7 15 15 11 15

  16. The Greedy Algorithm in Action Node 1 2 3 4 5 6 7 First 1 4 3 4 5 4 7 10 10 8 8 2 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 5 7 5 3 7 15 15 11 16

  17. The Greedy Algorithm in Action Node 1 2 3 4 5 6 7 First 1 4 3 4 5 45 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 5 7 7 5 3 7 15 15 11 17

  18. The Greedy Algorithm in Action Node 1 2 3 4 5 6 7 First 1 45 4 5 45 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 3 5 7 7 5 3 7 15 15 11 18

  19. 3 5 7 The Greedy Algorithm in Action Node 1 2 3 4 5 6 7 First 1 44 4 4 4 4 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 3 5 5 7 7 5 3 7 15 15 11 19

  20. 5 7 The Greedy Algorithm in Action Node 1 2 3 4 5 6 7 First 4 4 4 4 4 4 4 10 10 8 8 2 4 6 4 2 6 35 35 15 15 1 1 1 25 25 20 20 30 30 17 17 21 21 11 40 40 3 3 5 7 5 3 7 15 15 11 20

  21. Prim’s Algorithm in Action 10 8 2 4 4 6 2 6 35 15 1 1 25 20 30 17 21 11 40 3 5 7 5 3 7 15 The minimum cost arc from yellow nodes to green nodes can be found by placing arc values in a priority queue.

  22. 10 25 Prim’s Algorithm in Action 8 10 2 2 4 4 6 2 6 35 35 15 1 25 1 20 30 17 21 11 40 3 5 7 5 3 7 15

  23. 8 30 20 21 Prim’s Algorithm in Action 8 10 10 10 2 2 4 4 4 6 2 6 35 35 15 1 25 25 1 30 17 20 21 11 40 3 5 7 5 3 7 15

  24. 15 17 Prim’s Algorithm in Action 8 8 8 10 10 10 2 2 4 4 4 6 6 2 6 35 35 15 1 25 25 1 30 30 17 20 20 21 21 11 40 3 5 7 5 3 7 15

  25. 11 15 Prim’s Algorithm in Action 8 8 8 10 10 10 2 2 4 4 4 6 6 2 6 35 35 15 15 15 1 25 25 1 30 30 17 17 20 20 21 21 11 40 3 5 5 7 5 3 7 15

  26. 11 15 Prim’s Algorithm in Action 8 8 8 10 10 10 2 2 4 4 4 6 6 2 6 35 35 15 15 15 1 25 25 1 30 30 17 17 20 20 21 21 11 40 3 5 5 7 5 3 7 15

  27. Prim’s Algorithm in Action 8 8 8 10 10 10 2 2 4 4 4 6 6 2 6 35 35 15 15 15 1 25 25 1 30 30 17 17 20 20 21 21 11 11 11 40 3 5 5 7 7 5 3 7 15 15

  28. Prim’s Algorithm in Action 8 8 8 10 10 10 2 2 4 4 4 6 6 2 6 35 35 15 15 15 1 25 25 1 30 30 17 17 20 20 21 21 11 11 11 40 3 3 5 5 7 7 5 3 7 15 15 15

  29. Prim’s Algorithm in Action 8 8 8 10 10 10 2 2 4 4 4 6 6 2 6 35 35 15 15 15 1 25 25 1 30 30 17 17 20 20 21 21 11 11 11 40 3 3 5 5 7 7 5 3 7 15 15 15

  30. Prim’s Algorithm in Action 8 8 8 10 10 10 2 2 4 4 4 6 6 2 6 35 35 15 15 15 1 25 25 1 30 30 17 17 20 20 21 21 11 11 11 40 3 3 5 5 7 7 5 3 7 15 15 15

  31. Sollin’s Algorithm in Action 10 8 2 2 4 4 4 6 6 2 6 35 15 1 1 1 25 20 30 17 21 40 3 3 5 5 7 7 5 3 7 11 15 Treat all nodes as singleton components, and then select the min cost arc leaving the component.

  32. Sollin’s Algorithm in Action 10 8 2 4 4 6 6 2 6 35 15 1 1 25 20 30 17 21 40 3 3 5 5 7 7 5 3 7 11 15 Find the min cost edge out of each component

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