1. Breadth first search animation
and 6.855J
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
pred(1) = 0
next := 1 order(next) = 1
LIST:= {1}
Unmark all nodes in N;
Mark node s
LIST 1
next 1
Breadth first search animation

3. Breadth first search animation
Select a node i in LIST 1 2 4 5 3 6 9 7 8 1 1 1
In breadth first search, i is the first node in LIST
LIST 1
next 1
Breadth first search animation

4. If node i is incident to an admissible arc…2 4 2 2 8 1 1 1 1 5 7
Mark Node j
pred(j) := i
Select an admissible arc (i,j)
Next := Next + 1
order(j) := next
add j to LIST 9 3 6
LIST 1 2 1 2
next
Breadth first search animation

5. If node i is incident to an admissible arc…2 4 2 2 8 1 1 1 1 5 5 7 3
Mark Node j
pred(j) := i
Next := Next + 1
order(j) := next
add j to LIST
Select an admissible arc (i,j) 9 3 6
LIST 1 2 5 2 3
next
Breadth first search animation

6. If node i is incident to an admissible arc…2 4 2 2 8 1 1 1 1 5 5 7 3
Select an admissible arc (i,j)
Mark Node j
pred(j) := i
Next := Next + 1
order(j) := next
add j to LIST 9 3 3 6 4
LIST 1 2 5 3 3 4 2
next
Breadth first search animation

7. If node i is not incident to an admissible arc…2 4 2 2 8 1 1 1 1 1 5 5 7 3 9
Delete node i from LIST 3 3 6 4
LIST 1 2 5 3 4 3 2
next
Breadth first search animation

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

9. If node i is incident to an admissible arc…5 2 4 4 2 2 2 8 1 1 1 5 5 7 3
Mark Node j
pred(j) := i
Select an admissible arc (i,j)
Next := Next + 1
order(j) := next
add j to LIST 9 3 3 6 4
LIST 1 2 5 3 4 5 3 4 2
next
Breadth first search animation

10. If node i is not incident to an admissible arc…5 2 4 4 2 2 2 2 8 1 1 1 5 5 7 3
Delete node i from LIST 9 3 3 6 4
LIST 1 2 5 3 4 5 2 3 4
next
Breadth first search animation

11. Breadth first search animation
Select a node 5 2 4 4 2 2 2 8 1 1 1 5 5 5 7 3
The first node on LIST becomes node i 9 3 3 6 4
LIST 1 2 5 3 4 5 2 3 4
next
Breadth first search animation

12. If node i is incident to an admissible arc…5 2 4 4 2 2 2 8 1 1 1 5 5 5 7 3
Mark Node j
pred(j) := i
Select an admissible arc (i,j)
Next := Next + 1
order(j) := next
add j to LIST 9 3 3 6 6 4 6
LIST 1 2 5 3 4 6 6 3 2 5 4
next
Breadth first search animation

13. If node i is not incident to an admissible arc…5 2 4 4 2 2 2 8 1 1 1 5 5 5 5 7 3
Delete node i from LIST 9 3 3 6 6 4 6
LIST 1 2 5 3 4 6 6 2 5 3 4
next
Breadth first search animation

14. Breadth first search animation
Select node 3 5 2 4 4 2 2 2 8 1 1 1 5 5 5 5 7 3
node 3 is not incident to any admissible arcs
delete node 3 from LIST 9 3 3 3 3 6 6 4 6
LIST 1 2 5 3 4 6 4 2 3 6 5
next
Breadth first search animation

15. Breadth first search animation
Select a node 5 2 4 4 4 2 2 8 1 1 1 5 5 7 3
i : = 4 9 3 3 6 6 4 6
LIST 1 2 5 3 4 6 2 6 3 4 5
next
Breadth first search animation

16. If node i is incident to an admissible arc…5 2 4 4 4 7 2 2 8 8 1 1 1 5 5 7 3
Mark Node j
pred(j) := i
Select an admissible arc (i,j)
Next := Next + 1
order(j) := next
add j to LIST 9 3 3 6 6 4 6
LIST 1 2 5 3 4 6 8 7 3 2 6 4 5
next
Breadth first search animation

17. If node i is not incident to an admissible arc…5 2 4 4 4 4 7 2 2 8 8 1 1 1 5 5 7 3
Delete node i from LIST 9 3 3 6 6 4 6
LIST 1 2 5 3 4 6 8 7 3 2 6 4 5
next
Breadth first search animation

18. Breadth first search animation
Select node i 5 2 4 4 7 2 2 8 8 1 1 1 5 5 7 3
i := 6 9 3 3 6 6 6 4 6
LIST 1 2 5 3 4 6 8 7 2 3 6 4 5
next
Breadth first search animation

19. If node i is incident to an admissible arc…5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3
Select an admissible arc (i,j)
Next := Next + 1
order(j) := next
add j to LIST
Mark Node j
pred(j) := i 9 3 3 6 6 6 4 6
LIST 1 2 5 3 4 6 8 7 5 4 3 6 2 7 8
next
Breadth first search animation

20. If node i is incident to an admissible arc…5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3
Mark Node j
pred(j) := i
Select an admissible arc (i,j)
Next := Next + 1
order(j) := next
add j to LIST 9 9 3 3 6 6 6 4 9 6
LIST 1 2 5 3 4 6 8 7 9 5 9 8 2 4 6 3 7
next
Breadth first search animation

21. If node i is not incident to an admissible arc…5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3
Delete node i from LIST 9 9 3 3 6 6 6 6 4 9 6
LIST 1 2 5 3 4 6 8 7 9 2 9 8 4 6 3 5 7
next
Breadth first search animation

22. Breadth first search animation
Select node 8 5 2 4 4 7 2 2 8 8 8 8 1 8 1 1 5 5 7 7 3
node 8 is not incident to an admissible arc; delete it from LIST 9 9 3 3 6 6 6 6 4 9 6
LIST 1 2 5 3 4 6 8 7 9 9 3 2 8 7 4 6 5
next
Breadth first search animation

23. Breadth first search animation
Select node 7 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 7 7 3
node 7 is not incident to an admissible arc; delete it from LIST 9 9 3 3 6 6 6 6 4 9 6
LIST 1 2 5 3 4 6 8 7 9 9 3 2 8 7 4 6 5
next
Breadth first search animation

24. Breadth first search animation
Select node 9 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3
node 9 is not incident to an admissible arc; delete it from LIST 9 9 9 9 3 3 6 6 6 6 4 9 6
LIST 1 2 5 3 4 6 8 7 9 9 3 2 8 7 4 6 5
next
Breadth first search animation

25. Breadth first search animation
THE END
Breadth first search animation