Which of the following problems is solved by using Branch and Bound method?ans.travelling salesman problemDFSBFSprim's algorithm Previous Marked for Review Next

The Branch and Bound method is used to solve the Travelling Salesman Problem.

Here's a step-by-step explanation:

1. The Travelling Salesman Problem (TSP) is a classic algorithmic problem in the field of computer science and operations research. It focuses on optimization. In this problem, a salesman is given a list of cities, and must determine the shortest possible route that allows him to visit each city once and return to his original location.

2. The Branch and Bound method is an algorithmic approach used to solve optimization problems, like the TSP. It involves partitioning the problem into a collection of smaller problems (branching) and then solving these smaller problems to find the optimal solution (bounding).

3. The method starts with a calculation of a lower bound (a route that is potentially the shortest) for the first city. This is usually done using a method like the Greedy algorithm.

4. The algorithm then creates subproblems (branches) by including the next city in the route. For each of these subproblems, it calculates a lower bound on the best possible solution (the bound).

5. If the lower bound of a subproblem is greater than the best known solution, that subproblem is discarded as it cannot lead to a better solution (this is the bounding part of the algorithm).

6. The algorithm continues branching and bounding until it has found the shortest possible route, i.e., until all cities have been included in the route.

So, the Branch and Bound method is a systematic way to solve problems like the TSP by exploring the solution space in a structured manner, and discarding solutions that cannot lead to an optimal solution as early as possible.