It can be shown that the problem is inapproximable, as an epsilon-approximation algorithm would prove imply that there are polynomial-time algorithms for other NP-complete problems.
A crude branch-and-bound backtracking algorithm can be developed from a similar algorithm for the Hamilton cycle problem, but the Lin-Kernighan algorithm, which relies on lambda-change, is probably the best heuristic known for this problem. It can be shown that the problem is inapproximable, as an epsilon-approximation algorithm would prove imply that there are polynomial-time algorithms for other NP-complete problems. FTP, identify this most famous example of an NP-complete problem, in which a certain businessman would like to find the shortest distance needed to tour a set of cities.
A crude branch-and-bound backtracking algorithm can be developed from a similar algorithm for the Hamilton cycle problem, but the Lin-Kernighan algorithm, which relies on lambda-change, is probably the best heuristic known for this problem.
traveling salesman problem