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## What is the example of travelling salesman problem?

Problem Statement A traveler needs to visit all the cities from a list, where distances between all the cities are known and each city should be visited just once. What is the shortest possible route that he visits each city exactly once and returns to the origin city?

What algorithm is best for travelling salesman problem?

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 does the travelling salesman problem work?

The traveling salesman problem is a classic problem in combinatorial optimization. This problem is to find the shortest path that a salesman should take to traverse through a list of cities and return to the origin city. The list of cities and the distance between each pair are provided.

### Is traveling salesman problem solvable?

Of course, this problem is solvable by finitely many trials. Rules which would push the number of trials below the number of permutations of the given points, are not known.

How can we reduce particular column in Travelling salesman problem?

Column Reduction- Select the least value element from that column. Subtract that element from each element of that column.

How do you reduce the particular column in a Travelling salesperson problem?

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.

## How can we reduce the particular column in traveling salesman problem?

Column Reduction-

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

Can TSP be solved?

This means that TSP is classified as NP-hard because it has no “quick” solution and the complexity of calculating the best route will increase when you add more destinations to the problem. The problem can be solved by analyzing every round-trip route to determine the shortest one.

Has traveling salesman been solved?

Scientists in Japan have solved a more complex traveling salesman problem than ever before. The previous standard for instant solving was 16 “cities,” and these scientists have used a new kind of processor to solve 22 cities. They say it would have taken a traditional von Neumann CPU 1,200 years to do the same task.

### Is traveling salesman solved?

Computer scientist Richard Karp, of the University of California at Berkeley, __showed that the traveling salesman problem is “NP-hard,” which means that it has no efficient algorithm (unless a famous conjecture called P=NP is true — but the majority of computer scientists now suspect that it is false).

Is TSP NP-hard?

Thus we can say that the graph G’ contains a TSP if graph G contains Hamiltonian Cycle. Therefore, any instance of the Travelling salesman problem can be reduced to an instance of the hamiltonian cycle problem. Thus, the TSP is NP-Hard.

Can quantum computers solve the traveling salesman problem?

A quantum computer can solve classes of problems that no classical computer can efficiently solve, and perhaps that will someday include the travelling salesman problem. When your brute force options are too expensive and an efficient algorithm eludes you, don’t give up on ever solving the problem altogether.

## Is traveling salesman NP-hard?

In fact, TSP belongs to the class of combinatorial optimization problems known as NP-complete. This means that TSP is classified as NP-hard because it has no “quick” solution and the complexity of calculating the best route will increase when you add more destinations to the problem.

Is travel salesman NP a problem?

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).

What type of problems can quantum computers solve?

The class of problems that can be efficiently solved by quantum computers is called BQP, for “bounded error, quantum, polynomial time”. Quantum computers only run probabilistic algorithms, so BQP on quantum computers is the counterpart of BPP (“bounded error, probabilistic, polynomial time”) on classical computers.

### Why is TSP not in NP?

Why is TSP not NP-complete? The simple answer is that it’s NP-hard, but it’s 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.

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). I thought for A to be reduced to B, B has to be as hard if not harder than A.

How do I prove my TSP is NP?

To prove TSP is NP-Complete, first we have to prove that TSP belongs to NP. In TSP, we find a tour and check that the tour contains each vertex once. Then the total cost of the edges of the tour is calculated. Finally, we check if the cost is minimum.