# Is there an efficient algorithm for the traveling salesman problem?

## Is there an efficient algorithm for the traveling salesman problem?

The most efficient algorithm we know for this problem runs in exponential time, which is pretty brutal as we’ve seen. Unlike RSA encryption though, in the case of the Traveling Salesman Problem there is no modular arithmetic or turning factorization into period finding, as Shor’s algorithm does.

What is the traveling salesman problem in graph theory?

traveling salesman problem, an optimization problem in graph theory in which the nodes (cities) of a graph are connected by directed edges (routes), where the weight of an edge indicates the distance between two cities.

How can we apply approximation algorithm to solve traveling salesman problem?

Travelling Salesman Problem | Set 2 (Approximate using MST)

1. Algorithm:
2. 1) Let 1 be the starting and ending point for salesman.
3. 2) Construct MST from with 1 as root using Prim’s Algorithm.
4. 3) List vertices visited in preorder walk of the constructed MST and add 1 at the end.

### How does 2 Opt algorithm work?

The 2-opt algorithm works as follows: take 2 arcs from the route, reconnect these arcs with each other and calculate new travel distance. If this modification has led to a shorter total travel distance the current route is updated. The algorithm continues to build on the improved route and repeats the steps.

Is Travelling salesman problem dynamic programming?

Solution. Travelling salesman problem is the most notorious computational problem. We can use brute-force approach to evaluate every possible tour and select the best one. Instead of brute-force using dynamic programming approach, the solution can be obtained in lesser time, though there is no polynomial time algorithm …

Is TSP NP-hard or NP-complete?

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.

## 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).

What is traveling salesman problem explain with example?

For example, consider the graph shown in the figure on the right side. A TSP tour in the graph is 1-2-4-3-1. The cost of the tour is 10+25+30+15 which is 80. The problem is a famous NP-hard problem.

What do you understand by Travelling Salesman Problem explain its algorithm with example?

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.

### What approximation algorithm is used to construct the solution for Travelling Salesman Problem Mcq?

Accepted Answers: Nearest Neighbour Heuristic is used to solve a Travelling Salesman Problem.

Is 3 Opt better than 2-opt?

In optimization, 3-opt is a simple local search algorithm for solving the travelling salesperson problem and related network optimization problems. Compared to the simpler 2-opt algorithm, it is slower but can generate higher-quality solutions. . Iterated 3-opt has a higher time complexity.

What is the travelling salesman problem?

Travelling Salesman Problem 1 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. 2 Solution. Travelling salesman problem is the most notorious computational problem. 3 Analysis. There are at the most 2 n. 4 Example.

## Is there a polynomial time algorithm to find the weighted edges?

Instead of brute-force using dynamic programming approach, the solution can be obtained in lesser time, though there is no polynomial time algorithm. Let us consider a graph G = (V, E), where V is a set of cities and E is a set of weighted edges. An edge e (u, v) represents that vertices u and v are connected.

How can we evaluate every possible tour in a graph?

We can use brute-force approach to evaluate every possible tour and select the best one. For n number of vertices in a graph, there are (n – 1)! number of possibilities. Instead of brute-force using dynamic programming approach, the solution can be obtained in lesser time, though there is no polynomial time algorithm.