2. What are the differences between 'Backtracking'
and 'Branch & Bound' Algorithm techniques?
Backtracking
[1] It is used to find all possible
solutions available to the problem.
[2] It traverse tree by DFS (Depth First
Search).
[3] It realizes that it has made a bad
choice & undoes the last choice by
backing up.
[4] It search the state space tree until it
found a solution.
[5] It involves feasibility function
Branch-and-Bound
[1] It is used to solve optimization problem.
[2] It may traverse the tree in any manner,
DFS or BFS.
[3] It realizes that it already has a better
optimal solution that the pre-solution leads to
so it abandons that pre-solution.
[4] It completely searches the state space tree
to get optimal solution.
[5] It involves bounding function.
3. Here is the state space tree for n=4 (Using Branch And Bound)
4. What is traveling salesman problem?
• Let us look at a situation that there are 5 cities,
which are represented as NODES.
• There is a Person at NODE-1
• This person has to reach each nodes one and only
ones and come back to original (starting) position
• This process has to occur with minimum cost or
minimum distance travelled.
• Note that starting point can start with any Node. For
Example:
1-2-4-5-3-1
1-5-2-3-4-1
5. How to compute the cost of each node?
• A row/column is said to be reduce iff it contains at least one zero and
all remaining entries are non-negative.
• A matrix is reduced iff every row and column is reduced.
Rules of reduced cost matrix :
1. Change all entries in row i and column j from A to inf
2. Set A[j,1] to inf
3. Reduce all rows and columns in the resulting except for rows and
column containing only inf.
4. Cost Function C(s)=C(R)+A[i,j]+ r [r – total reduce value]
![What are the differences between 'Backtracking'
and 'Branch & Bound' Algorithm techniques?
Backtracking
[1] It is used to find all possible
solutions available to the problem.
[2] It traverse tree by DFS (Depth First
Search).
[3] It realizes that it has made a bad
choice & undoes the last choice by
backing up.
[4] It search the state space tree until it
found a solution.
[5] It involves feasibility function
Branch-and-Bound
[1] It is used to solve optimization problem.
[2] It may traverse the tree in any manner,
DFS or BFS.
[3] It realizes that it already has a better
optimal solution that the pre-solution leads to
so it abandons that pre-solution.
[4] It completely searches the state space tree
to get optimal solution.
[5] It involves bounding function.](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)