What is the difference between dynamic programming and branch and bound?

Question

I only know that by branch and bound, one can REDUCE the procedure to obtain a solution, but that only helps for problems which have a solution space tree.

Answer 1

Dynamic Programming

Dynamic programming (usually referred to as DP ) is a very powerful technique to solve a particular class of problems. It demands very elegant formulation of the approach and simple thinking and the coding part is very easy.
The idea is very simple, If you have solved a problem with the given input, then save the result for future reference, so as to avoid solving the same problem again. Shortly 'Remember your Past' .

If the given problem can be broken up in to smaller sub-problems and these smaller subproblems are in turn divided in to still-smaller ones, and in this process, if you observe some over-lappping subproblems, then its a big hint for DP. Also, the optimal solutions to the subproblems contribute to the optimal solution of the given problem ( referred to as the Optimal Substructure Property ).

There are two ways of doing this.

1.) Top-Down : Start solving the given problem by breaking it down. If you see that the problem has been solved already, then just return the saved answer. If it has not been solved, solve it and save the answer. This is usually easy to think of and very intuitive. This is referred to as Memoization.

2.) Bottom-Up : Analyze the problem and see the order in which the sub-problems are solved and start solving from the trivial subproblem, up towards the given problem. In this process, it is guaranteed that the subproblems are solved before solving the problem. This is referred to as Dynamic Programming.

Branch And Bound

• A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root.
  
• The algorithm explores branches of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated bounds on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm.
  

For more Information About Branch and Bound Please refer this link :

http://www.cs.umsl.edu/~sanjiv/classes/cs5130/lectures/bb.pdf