The travelling salesman problem

Abstract

In this chapter the author considers how to work out the shortest round-trip through a number of cities, a hard problem for which we do not know how to find an optimal solution. The author first demonstrates why a brute-force approach is disastrous, and he then shows how dynamic programming offers a significant improvement in running time. Finally he explains how a so-called approximation algorithm can find a tour that is maybe not the shortest one but one whose length usually is quite close to the optimum. © 2011 Springer-Verlag Berlin Heidelberg.