Question

determine whether the following statement is true or false.
the nearest neighbor method provides exact solutions to the traveling salesperson problems

choose the correct answer below.

a. the statement is true. the nearest neighbor method always gives the same circuit as the brute force method, and the brute force method always gives an optimal solution.

b. the statement is true. the nearest neighbor method is an algorithm that does not terminate until it produces the optimal solution.

c. the statement is false. once the number of vertices in a graph gets large, it is impossible to find the exact solution, so the nearest neighbor method would not work.

d. the statement is false. the nearest neighbor method is meant only to approximate the optimal solution

Explanation:

The Nearest Neighbor Method is a heuristic algorithm. Heuristic algorithms are designed to approximate solutions rather than guaranteeing exact (optimal) solutions. The Brute Force Method, which checks all possible circuits, gives the exact optimal solution but is computationally infeasible for large graphs. The Nearest Neighbor Method starts at a vertex and repeatedly moves to the nearest unvisited vertex. It can lead to non - optimal circuits, especially as the number of vertices increases.

Answer:

D. The statement is false. The Nearest Neighbor Method is meant only to approximate the optimal solution.