# What is the time complexity of TSP using branch and bound?

## What is the time complexity of TSP using branch and bound?

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

### Which is the best algorithm for TSP?

The Greedy Heuristic is again the winner of the shortest path, with a length of 72801 km. The nearest neighbor solution route is longer by 11,137 km but has less computation time. On the other hand, the Genetic algorithm has no guarantee of finding the optimal solution and hence its route is the longest (282866).

How do I reduce the particular column in TSP 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. This will create an entry ‘0’ in that column, thus reducing that column.

What is the branch and bound algorithm for TSP in operations research?

A “branch and bound” algorithm is presented for solving the traveling salesman problem. The set of all tours (feasible solutions) is broken up into increasingly small subsets by a procedure called branching. For each subset a lower bound on the length of the tours therein is calculated.

## How Travelling salesperson problem can be solved using branch and bound?

In order to solve the problem using branch n bound, we use a level order. First, we will observe in which order, the nodes are generated. While creating the node, we will calculate the cost of the node simultaneously. If we find the cost of any node greater than the upper bound, we will remove that node.

### Is traveling salesman NP-complete?

Traveling Salesman Optimization(TSP-OPT) is a NP-hard problem and Traveling Salesman Search(TSP) is NP-complete. However, TSP-OPT can be reduced to TSP since if TSP can be solved in polynomial time, then so can TSP-OPT(1).

How can we solve travel salesman problem using branch and bound in detail with an example?

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.

How can you reduce that particular row in Travelling salesperson using branch and bound?

In general, to get the lower bound of the path starting from the node, we reduce each row and column so that there must be at least one zero in each row and Column. We need to reduce the minimum value from each element in each row and column.

## Why is TSP not in NP?

Since it’s not in NP, it can’t be NP-complete. In TSP you’re looking for the shortest loop that goes through every city in a given set of cities. Since it takes exponential time to solve NP, the solution cannot be checked in polynomial time. Thus this problem is NP-hard, but not in NP.

### Which one is solved by branch and bound method?

Branch and bound is an algorithm design paradigm which is generally used for solving combinatorial optimization problems. These problems are typically exponential in terms of time complexity and may require exploring all possible permutations in worst case.

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