Bounding..Alogothim


A Maximization Problem P of n items has a Bounding function B. A brute force/exhaustive search solution for P has an order of growth of n^2 5^n . A solution is a vector (x1,x2,…xn), where xi=- 2,-1, 0, 1 or 2, i=1,n. P is to be solved using Backtracking/Branch and Bound. Answer the following:

1) What is the order of growth of the Backtracking solution?

2) What is the order of growth of the Branch and Bound solution?

3) If all partial solutions are feasible, what is the maximum number of pruned nodes? When does this case happen?

4) If all partial solutions are feasible, what is the minimum number of pruned nodes? When does this case happen?

5) Which is better Backtracking or Branch and Bound? Why?