1. Branch and bound branch and bound methods economize the search for the best trees by backing out of dead alleys.

2. The Traveling Salesman Problem the technique can be used to solve the traveling salesman problem.

3. The Traveling Salesman Problem d=5.4342 an arbitrary route.

4. The Traveling Salesman Problem d=2.8027 d=5.4342 greedy, starting from each point

5. The Traveling Salesman Problem d=2.8027 d=5.4342 d=2.7812 solution found by branch and bound

6. The Traveling Salesman Problem start 1 2 3 4 5 6 … 2 3 4 8 9 10 1,2,3,4,5,6,7,8,9,10 10 9 1,2,3,4,5,6,7,8,10,9 9 8 10 1,2,3,4,5,6,7,9,8,10 10 8 1,2,3,4,5,6,7,9,10,8 10 8 9 1,2,3,4,5,6,7,10,8,9 9 8 1,2,3,4,5,6,7,10,9,8 3 4 5 5 6 the problem as a decision tree with 3 628 800 (10!) paths

7. Branching and bounding B&B walk along the paths, and keep track of the distance travelled and the shortest route as yet

8. Branching and bounding distance=x distance>x and bound back out of lengthy paths

9. Branch and bound for parsimony a b c a d b c a c b d a c b d a c b e a c d e c e b d a e b d c a d b e a d c e b a d b e c a d b c e d e b c a e a b c d a e c d b b e c d a a b c d e a b c e d a b d e c a d b c

10. 5 8 7 9 9 9 9 9 11 9 10 8 11

11. Branch and bound for parsimony 5 8 7 9 9 9 9 9 11 9 10 8 11

12. Branch and bound for parsimony 5 8 7 9 9 9 9 9 11 9 10 8 11