Traveling Salesperson: Done another way.

1
Traveling SalespersonDone another way.

• Lecture 29
• CS 312

2
Tomorrow

• QA review section.
• No new material will be covered.

3
Questions?

• Homework from Friday?
• TSP using branch and bound?

4
Recap and Objectives

• On Friday, we solved TSP using branch and bound.
• Modeled the problem as starting at node i which
  node should be visited next to get the least
  bound?
• Today model TSP as if the edge between nodes
  j and k is included (for any j and k) what bound
  can be obtained?

5
New Search Tree
Use the same method for computing bounds.
Do include edge (i,j)
Do not include edge (i,j)
What happens to the matrix when an edge is
excluded?
6
Excluding an Edge
0
1
0
0
9
1
0
6
1
7
Which edge to consider

• Maximize exclude bound.
• Maximize the difference between the two.

8
Consider edge (3,2)
include (3,2)
exclude (3,2)
bound 22
bound 21
0
0
1
0
0
0
0
9
9
0
1
0
1
0
6
0
6
0
1
9
Consider edge (2,3)
bound 21
include (2,3)
exclude (2,3)
bound 21
bound 28
0
1
0
1
0
0
0
9
0
9
0
1
0
1
0
6
0
6
1
1
10
Consider edge (5,1)
bound 21
include (5,1)
exclude (5,1)
bound 30
bound 21
0
1
0
1
0
0
0
0
9
0
0
1
0
1
0
6
6
0
0
1
1
11
Tree so far
bound 21
include (5,1)
exclude (5,1)
bound 30
bound 21
12
Consider edge (2,5)
bound 21
include (2,5)
exclude (2,5)
bound 28
bound 21
1
1
0
0
0
0
0
0
1
0
0
6
0
0
1
1
13
Tree so far
21
include (5,1)
exclude (5,1)
30
21
include (2,5)
exclude (2,5)
28
21
14
Consider edge (3,2)
bound 21
include (3,2)
exclude (3,2)
bound 22
bound 21
1
0
0
0
0
0
0
0
0
15
Tree so far
21
include (5,1)
exclude (5,1)
30
21
include (2,5)
exclude (2,5)
28
21
include (3,2)
exclude (3,2)
21
22
16
Tree so far
21
include (5,1)
exclude (5,1)
30
21
include (2,5)
exclude (2,5)
28
21
include (3,2)
exclude (3,2)
0
21
22
...
include (4,3),(1,4)
0
21
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Things to ponder

• Under what conditions can a node be killed?
• Dont focus strictly on the bounds.
• Homework
• do the same TSP problem, but using the algorithm
  we discussed today.
• do it before Thanksgiving for max. effectiveness.