# Is traveling salesman problem NP-complete?

## Is traveling salesman problem NP-complete?

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.

Which of the following problems is NP-complete traveling salesman 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).

How would you show that the traveling salesman problem is in 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.

### What kind of problem is travelling salesman problem?

The traveling salesman problem (TSP) is an algorithmic problem tasked with finding the shortest route between a set of points and locations that must be visited. In the problem statement, the points are the cities a salesperson might visit.

Is Hamilton cycle and Travelling salesman problem NP-complete?

Therefore, Hamiltonian cycle is a NP-Complete problem.

Which of the following is NP complete problem?

Explanation: Hamiltonian circuit, bin packing, partition problems are NP complete problems.

#### What is TSP problem in AI?

Traveling Salesman Problem (TSP) You are given a list of n cities with the distance between any two cities. Now, you have to start with your office and to visit all the cities only once each and return to your office. What is the shortest path can you take? This problem is called the Traveling Salesman Problem (TSP).

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.

Is TSP problem Hamiltonian cycle?

The Hamiltonian Cycle Problem (HCP) and Travelling Salesman Problem (TSP) are long-standing and well-known NP-hard problems. The HCP is concerned with finding paths through a given graph such that those paths visit each node exactly once after the start, and end where they began (i.e., Hamiltonian cycles).

## How do you solve NP-complete problems?

NP-Completeness

1. Use a heuristic. If you can’t quickly solve the problem with a good worst case time, maybe you can come up with a method for solving a reasonable fraction of the common cases.
2. Solve the problem approximately instead of exactly.
3. Use an exponential time solution anyway.
4. Choose a better abstraction.

Is partition problem NP-complete?

Although the partition problem is NP-complete, there is a pseudo-polynomial time dynamic programming solution, and there are heuristics that solve the problem in many instances, either optimally or approximately. For this reason, it has been called “the easiest hard problem”.

Is Hamiltonian cycle NP-complete?

Conclusion: Since, the Hamiltonian Cycle is both, a NP-Problem and NP-Hard. Therefore, it is a NP-Complete problem.

### Why is the TSP important?

The importance of the TSP is that it is representative of a larger class of problems known as combinatorial optimization problems. The TSP problem belongs in the class of such problems known as NP-complete.

Is Hamilton cycle and travelling salesman problem NP-complete?

Is the traveling salesman problem NP-complete or P-complete?

In the early 1970s, the concept of P vs. NP problems created buzz in the theoretical computer science community. In 1972, Richard Karp demonstrated that the Hamiltonian cycle problem was NP-complete, implying that the traveling salesman problem was NP-hard. 4

#### What is the traveling salesman problem?

The traveling salesman problem (TSP) is a widely studied combinatorial optimization problem, which, given a set of cities and a cost to travel from one city to another, seeks to identify the tour that will allow a salesman to visit each city only once, starting and ending in the same city, at the minimum cost. 1

What is an example of NP-complete problem?

Then we have to find the shortest tour so that the travelling salesman can visit each and every city only once.” This travelling salesman problem is one of the examples of NP-Complete problems.

What is the cost matrix of the traveling salesman problem?

The cost matrix is given by where the cost of the edge joining node to node , denoted , is given in entry . In the context of the traveling salesman problem, the verticies correspond to cities and the edges correspond to the path between those cities.