Question

Consider this scenario: You are working for a company that manufactures and markets vacuum cleaners. You plan to expand your sales area, which will result in a doubling of the number of cities that must be visited by each of your salespeople. You have an algorithm for finding the optimal order of cities to visit for your salesmen to minimize their driving. This problem is known as the traveling salesman problem. The best known algorithm for the traveling salesman problem is θ(2^N) You point out that running the program that finds the optimal order for a salesperson to visit a list of cities is already slow, and that doubling the number of cities will make it even slower. Your boss agrees, and plans to buy a computer that is twice as fast as the one you are now using, which he claims will result in the same run time for the larger list of cities.

Answer 1

The best known algorithm for the traveling salesman problem has a run time of θ(2^N), where N is the number of cities.

Step-by-step explanation:

This question is about the traveling salesman problem, an algorithmic problem in computer science. The question discusses the impact of doubling the number of cities on the run time of the algorithm. The answer explains that the best known algorithm for the traveling salesman problem has a run time of θ(2^N), where N is the number of cities. Doubling the number of cities means the run time will also be doubled, so buying a computer that is twice as fast will not result in the same run time for the larger list of cities. Instead, the run time will still be slower than the initial run time.