# What is Travelling salesman problem using branch and bound?

## What is Travelling salesman problem using branch and bound?

Given a set of cities and distance between every pair of cities, the problem is to find the shortest possible tour that visits every city exactly once and returns to the starting point. For example, consider the graph shown in figure on right side.

**What is branch and bound algorithm for TSP?**

The branch-and-bound algorithm for the traveling salesman problem uses a branch-and-bound tree, like the branch-and-bound algorithms for the knapsack problem and for solving integer programs. • The node at the top of the tree is called the root. All edges (arrows) in the tree point downward.

### How can you reduce that particular row in Travelling salesman problem using branch and bound?

Reduce that particular column. Select the least value element from that column. Subtract that element from each element of that column….

- There is no need to reduce column-1.
- There is no need to reduce column-2.
- Reduce the elements of column-3 by 1.
- There is no need to reduce column-4.

**What is meant by branch and bound?**

Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. The algorithm explores branches of this tree, which represent subsets of the solution set.

#### What is the time complexity for Travelling salesman problem in branch and bound?

The time complexity of the program is O(n^2) as explained above for the row and column reduction functions.

**Where is branch and bound used?**

Branch and bound algorithms are used to find the optimal solution for combinatory, discrete, and general mathematical optimization problems. In general, given an NP-Hard problem, a branch and bound algorithm explores the entire search space of possible solutions and provides an optimal solution.

## Is the travelling salesman problem a branch or bound problem?

In this article we will briefly discuss about the travelling salesman problem and the branch and bound method to solve the same. What is the problem statement ?

**Which is the root node in the traveling salesman problem?**

1. The Root Node: Without loss of generality, we assume we start at vertex “0” for which the lower bound has been calculated above. Dealing with Level 2: The next level enumerates all possible vertices we can go to (keeping in mind that in any path a vertex has to occur only once) which are, 1, 2, 3… n (Note that the graph is complete).

### Which is the best way to solve the travelling salesman problem?

Reduce that particular row. Select the least value element from that row. Subtract that element from each element of that row. This will create an entry ‘0’ in that row, thus reducing that row. Reduce the elements of row-1 by 4. Reduce the elements of row-2 by 5. Reduce the elements of row-3 by 6. Reduce the elements of row-4 by 2.

**Which is an example of branch and bound?**

For example, in Job Assignment Problem, we get a lower bound by assigning least cost job to a worker. In branch and bound, the challenging part is figuring out a way to compute a bound on best possible solution. Below is an idea used to compute bounds for Traveling salesman problem.