Question

III. A Last Problem: The speed of computers has increased greatly over the history of computing. The traveling salesman problem attempts to find a pathway for a salesman to visit all of the cities on his route using the shortest distance. The brute force method for solving this problem looks at all possible permutations of the cities. There are n! such permutations (where n! n* (n-1)* (n-2) *...*1). Thus, 5! 120. Current computers are running with clock speeds in the GigaHz range (10,000,000 times faster than the earliest computers) and they still are not able to solve the traveling salesmen problem using this brute force method for moderate values of n (like 50). If technology keeps moving ahead at the current rate, will this problem soon become feasible yes or no)? Back up your answer with some sample numbers concerning factorials and speed of computers.

Answer 1