# How can you reduce that particular row in traveling salesperson problem using branch and bound?

## How can you reduce that particular row in traveling salesperson problem using branch and bound?

Row Reduction-

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

## What is the example of Travelling salesman problem?

For example, consider the graph shown in the figure on the right side. A TSP tour in the graph is 1-2-4-3-1. The cost of the tour is 10+25+30+15 which is 80. The problem is a famous NP-hard problem.

How can we solve Travelling salesman problem?

To solve the TSP using the Brute-Force approach, you must calculate the total number of routes and then draw and list all the possible routes. Calculate the distance of each route and then choose the shortest one—this is the optimal solution. This method breaks a problem to be solved into several sub-problems.

How do you calculate lower bound in travel salesman problem?

A lower bound can be found by removing a vertex, then finding a minimum spanning tree: Use Prim’s or Kruskal’s algorithm to find the length of the minimum spanning tree. Add to this the lengths of the two shortest edges connected to the missing vertex.

### What is the best way of representing the Travelling salesman problem?

The key to this method is to always visit the nearest destination and then go back to the first city when all other cities are visited. To solve the TSP using this method, choose a random city and then look for the closest unvisited city and go there. Once you have visited all cities, you must return to the first city.

### Is travelling salesman problem dynamic programming?

Travelling Salesman Problem uses Dynamic programming with masking algorithm.

How to solve the traveling salesman problem using branch and bound?

Traveling 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. A TSP tour in the graph is 0-1-3-2-0.

Which is the algorithm for the traveling salesman problem?

“branch and bound” algorithm is presented for solving the travel-ing salesman problem. The set of all tours (feasible solutions) is broken up into increasingly small subsets by a procedure called branch-ing. For each subset a lower bound on the length of the tours therein is calculated. Eventually, a subset is found which contains a single

## 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 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.