# Is Travelling salesman problem is NP-complete or NP-hard?

## Is Travelling salesman problem is NP-complete or 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.

### Why travel salesman problem is NP-complete?

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.

How do you prove traveling salesman is NP-complete?

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.

Can NP-hard reduce to NP-complete?

Can an NP-Hard problem be reduced to an NP problem, which is not already an NP-Complete problem? No. Suppose that X is NP-hard and it reduces to Y. By definition of NP-hardness, every problem in NP reduces to X.

## How can we reduce the particular column in Travelling 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.

### What is reduction in NP completeness explain with an example?

Reductions: The class of NP-complete problems consists of a set of decision problems (languages) (a subset of the class NP) that no one knows how to solve efficiently, but if there were a polynomial time solution for even a single NP-complete problem, then every problem in NP would be solvable in polynomial time.

How to solve the traveling salesman problem?

– The search system should be globally convergent. – The search system should be deterministic and have a rigorous guarantee for finding all globally optimal solutions without excessive computational burden. – The optimality criterion in the system must be based on information on the global behavior of the search system.

What are NP hard problems?

– given an instance x of X, it produces an instance y of Y – It runs in time polynomial. – Answer to x YES if and only if answer to y is YES.

## What is NP hard problem?

Approximate computing

• Configuration
• Cryptography
• Data mining
• Decision support
• Phylogenetics
• Planning
• Process monitoring and control
• Rosters or schedules
• Routing/vehicle routing
• ### What is the traveling salesman problem?

Travelling Salesman Problem (TSP) : Given a set of cities and distances between every pair of cities, the problem is to find the shortest possible route that visits every city exactly once and returns to the starting point. Note the difference between Hamiltonian Cycle and TSP. The Hamiltonian cycle problem is to find if there exists a tour that visits every city exactly once.