which of the following statements correctly describes the traveling salesman problem
The correct statement that describes the traveling salesman problem (TSP) is:
The TSP is a classic optimization problem in computer science and mathematics, where the goal is to find the shortest possible route for a salesman to travel between a set of cities and return to the starting city, visiting each city exactly once.
The traveling salesman problem (TSP) is a well-known optimization problem in computer science and mathematics. The problem can be stated as follows:
"Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the starting city?"
Among the options provided, the correct statement describing the traveling salesman problem is:
- The traveling salesman problem is an optimization problem that seeks to find the shortest possible route to visit a given list of cities exactly once.
The Traveling Salesman Problem (TSP) is a classic optimization problem in computer science and mathematics. It can be defined as follows: given a list of cities and the distances between each pair of cities, the objective is to find the shortest possible route that visits each city exactly once and returns to the starting city.
Statement: "The Traveling Salesman Problem is an NP-hard problem."
Explanation: This statement correctly describes the nature of the TSP. In computer science, the class of problems known as NP-hard represents a set of problems that are considered highly complex and have no known efficient algorithm to solve them. The TSP is one such problem, which means there is no known algorithm that can find the optimal solution for a large number of cities in a reasonable amount of time. However, approximate algorithms and heuristics exist to find near-optimal solutions.
To determine if a given problem is NP-hard, one usually needs to show that it is at least as hard as another known NP-hard problem. In the case of the TSP, it has been proven that if there is an efficient algorithm to solve the TSP, then there is an efficient algorithm to solve any NP-hard problem. Hence, the TSP is considered an NP-hard problem.
In summary, the statement correctly describes the TSP as an NP-hard problem, indicating its complexity and lack of known efficient algorithms for solving it optimally.