1. Breadth first search animation
Network Optimization
Breadth First Search
Get ahold of a network, and use the same network to illustrate the shortest path problem for communication newtorks, the max flow problem, the minimum cost flow problem, and the multicommodity flow problem. This will be a very efficient way of introducing the four problems. (Perhaps under 10 minutes of class time.)
Breadth first search animation

2. Breadth first search animation
Initialize 1 2 4 5 3 6 9 7 8 1 2 4 5 3 6 9 7 8 1 1
Unmark all nodes in N;
Mark node 1 and add it to LIST.
LIST 1
Breadth first search animation

3. Breadth first search animation
Select node 1 1 2 4 5 3 6 9 7 8 1 2 1 1 1 3
Select the first node in LIST.
Arc numbers for arcs in A(i) refer to the order in which arcs of A(i) are scanned.
LIST 1
Breadth first search animation

4. Breadth first search animation
Scan arcs (1,2) 2 4 2 2 8 1 2 1 1 1 1 5 7
Find an admissible arc 3 9 3 6
LIST 1 2
Breadth first search animation

5. Breadth first search animation
Scan arc (1,5) 2 4 2 2 8 1 2 1 1 1 1 5 5 7 3
Select node 1 and find an admissible arc. 3 9 3 6
LIST 1 2 5
Breadth first search animation

6. Breadth first search animation
Scan arc (1,3) 2 4 2 2 8 1 2 1 1 1 1 5 5 7 3
Select node 1 and find an admissible arc. 3 9 3 3 6 4
LIST 1 2 5 3
Breadth first search animation

7. Breadth first search animation
Delete Node 1 from LIST 2 4 2 2 8 1 1 1 1 1 5 5 7 3
Delete node 1 from LIST 9 3 3 6 4
LIST 1 2 5 3
Breadth first search animation

8. Breadth first search animation
Select Node 2 1 2 4 2 2 2 8 2 1 1 1 1 1 5 5 7 3
Select first node on LIST 9 3 3 6 4
LIST 1 2 5 3
Breadth first search animation

9. Breadth first search animation
Scan arc (2, 4) 5 1 2 4 4 2 2 2 8 2 1 1 1 5 5 7 3
Select an admissible arc 9 3 3 6 4
LIST 1 2 5 3 4
Breadth first search animation

10. Breadth first search animation
Scan arc (2, 5) 5 1 2 4 4 2 2 2 8 2 1 1 1 5 5 7 3
Ignore any scanned arcs out of node 2 that are not admissible. 9 3 3 6 4
LIST 1 2 5 3 4
Breadth first search animation

11. Breadth first search animation
Delete node 2 5 2 4 4 2 2 2 2 8 1 1 1 5 5 7 3
Delete node 2 from LIST 1 9 3 3 6 4
LIST 2 5 3 4
Breadth first search animation

12. Breadth first search animation
Select node 5 5 2 4 4 2 2 2 8 1 1 1 5 5 5 7 3 1
Select the first node on LIST 9 3 3 6 4
LIST 5 3 4
Breadth first search animation

13. Breadth first search animation
Scan arc (5,6) 5 2 4 4 2 2 2 8 1 1 1 5 5 5 7 3
Find an admissible arc 1 9 3 3 6 6 4 6
LIST 5 3 4 6
Breadth first search animation

14. Breadth first search animation
Delete node 5 5 2 4 4 2 2 2 8 1 1 1 5 5 5 5 7 3 1
Delete node 5 from LIST 2 9 3 3 6 6 4 6
LIST 5 3 4 6
Breadth first search animation

15. Breadth first search animation
Select node 3 5 2 4 4 2 2 2 8 1 1 1 5 5 5 5 7 3 1
Select first node on LIST 2 9 3 3 3 6 6 4 6
LIST 3 4 6
Breadth first search animation

16. Breadth first search animation
Scan arcs out of node 3 5 2 4 4 2 2 2 8 1 1 1 5 5 5 5 7 3 1
Ignore any scanned arc that is not admissible. 2 9 3 3 3 6 6 4 6
LIST 3 4 6
Breadth first search animation

17. Breadth first search animation
Delete node 3 5 2 4 4 2 2 2 8 1 1 1 5 5 5 5 7 3
Delete node 3 from LIST 9 3 3 3 3 6 6 4 6
LIST 3 4 6
Breadth first search animation

18. Breadth first search animation
Select node 4 5 1 2 4 4 4 2 2 8 2 1 1 1 5 5 7 3
Select the first node on LIST 9 3 3 6 6 4 6
LIST 4 6
Breadth first search animation

19. Breadth first search animation
Scan arc (4, 8) 5 1 2 4 4 4 7 2 2 8 8 2 1 1 1 5 5 7 3
Look for an admissible arc. 9 3 3 6 6 4 6
LIST 1 2 5 3 4 6 8
Breadth first search animation

20. Breadth first search animation
Scan arc (4, 5) 5 1 2 4 4 4 7 2 2 8 8 2 1 1 1 5 5 7 3
Look for an admissible arc 9 3 3 6 6 4 6
LIST 4 6 8
Breadth first search animation

21. Breadth first search animation
Delete Node 4 5 2 4 4 4 4 7 2 2 8 8 1 1 1 5 5 7 3
Delete node 4 from LIST 9 3 3 6 6 4 6
LIST 4 6 8
Breadth first search animation

22. Breadth first search animation
Select node 6 5 2 4 4 7 2 2 8 8 1 1 1 5 5 7 3 1
Select the first node on LIST 2 9 3 3 6 6 6 4 6
LIST 6 8
Breadth first search animation

23. Breadth first search animation
Scan arc (6,7) 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3 1
Scan arcs out of node 6 one at a time. 2 9 3 3 6 6 6 4 6
LIST 1 2 5 3 4 6 8 7
Breadth first search animation

24. Breadth first search animation
Scan arc (6,9) 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3 1
Scan arcs out of node 6 one at a time. 2 9 9 3 3 6 6 6 4 9 6
LIST 6 8 7 9
Breadth first search animation

25. Breadth first search animation
Delete node 6 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3
Delete node 6 from LIST 9 9 3 3 6 6 6 6 4 9 6
LIST 6 8 7 9
Breadth first search animation

26. Breadth first search animation
Select node 8 5 2 4 4 7 2 2 8 8 8 1 8 1 1 5 5 7 7 3
Select first node on LIST 9 9 3 3 6 6 6 6 4 9 6
LIST 8 7 9
Breadth first search animation

27. Breadth first search animation
Delete node 8 5 2 4 4 7 2 2 8 8 8 8 1 8 1 1 5 5 7 7 3
Delete node 8 9 9 3 3 6 6 6 6 4 9 6
LIST 8 7 9
Breadth first search animation

28. Breadth first search animation
Select node 7 5 2 4 4 7 2 2 8 8 2 3 1 1 8 1 1 5 5 7 7 7 3
Select first node on LIST 9 9 3 3 6 6 6 6 4 9 6
LIST 7 9
Breadth first search animation

29. Breadth first search animation
Scan arcs out of node 7 5 2 4 4 7 2 2 8 8 2 3 1 1 8 1 1 5 5 7 7 7 3
Scan arcs out of node 7 one at a time. 9 9 3 3 6 6 6 6 4 9 6
LIST 7 9
Breadth first search animation

30. Breadth first search animation
Delete node 7 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 7 7 3
Delete node 7 from LIST 9 9 3 3 6 6 6 6 4 9 6
LIST 7 9
Breadth first search animation

31. Breadth first search animation
Select node 9 5 2 4 4 7 2 2 8 8 2 1 8 1 1 5 5 7 7 3
Select the first node on LIST 1 9 9 9 3 3 6 6 6 6 4 9 6
LIST 9
Breadth first search animation

32. Breadth first search animation
Scan arcs out of node 9 5 2 4 4 7 2 2 8 8 2 1 8 1 1 5 5 7 7 3
Scan arcs out of node 9, one at a time 1 9 9 9 3 3 6 6 6 6 4 9 6
LIST 9
Breadth first search animation

33. Breadth first search animation
Delete node 9 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3
Delete node 9 from LIST 9 9 9 9 3 3 6 6 6 6 4 9 6
LIST 9
Breadth first search animation

34. Breadth first search animation
THE END
Breadth first search animation

35. 15.082J / 6.855J / ESD.78J Network Optimization
MITOpenCourseWare
15.082J / 6.855J / ESD.78J Network Optimization
Fall 2010
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