What is the example of Travelling salesman problem?
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 is Travelling Salesman problem in mathematics?
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.
Is Travel salesman a problem?
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 NP a traveling salesman?
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 Travelling salesman problem in assignment?
A traveling salesman problem is to determine a set of n elements of this matrix , one in each row and one in each column, so as to minimize the sum of elements determined above. Traveling salesman problem is similar to the assignment problem, but here two extra restrictions are imposed.
What is Travelling salesman problem and how is it modeled as a graph problem?
The traveling nalesman problem (TSP) is to find a tour of minimal cost. The TSP can be modeled as a graph problem by considering a complete graph G = /V, E), and assigning each edge uu E E the cost o., A tour is then a circuit in G that meets every node. In this context, tours are sometimes called Eamiltonian c~rcuits.
Is traveling salesman NP-hard?
It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem and the vehicle routing problem are both generalizations of TSP.
Is traveling salesman NP-complete?
What happens if P NP is true?
If P equals NP, every NP problem would contain a hidden shortcut, allowing computers to quickly find perfect solutions to them. But if P does not equal NP, then no such shortcuts exist, and computers’ problem-solving powers will remain fundamentally and permanently limited.