The Traveling Salesman Problem is an NP-hard problem, which means that there is no known algorithm that can solve it in polynomial time. The best-known algorithm for solving the problem is the Held-Karp algorithm, which has a time complexity of O(n^2 * 2^n), where n is the number of cities in the problem. While this algorithm is an improvement over brute-force methods, it is still not efficient enough to solve large instances of the problem in a reasonable amount of time.