About the Book

The Stony Brook Algorithm Repository

Steven Skiena
Stony Brook University
Dept. of Computer Science

1.5.4 Traveling Salesman Problem

INPUT                    OUTPUT

Input Description: A weighted graph G.

Problem: Find the cycle of minimum cost visiting all of the vertices of G exactly once.

Excerpt from The Algorithm Design Manual: The traveling salesman problem is the most notorious NP-complete problem. This is a function of its general usefulness, and because it is easy to explain to the public at large. Imagine a traveling salesman who has to visit each of a given set of cities by car.

Although the problem arises in transportation applications, its most important applications arise in optimizing the tool paths for manufacturing equipment. For example, consider a robot arm assigned to solder all the connections on a printed circuit board. The shortest tour that visits each solder point exactly once defines the most efficient path for the robot. A similar application arises in minimizing the amount of time taken by a graphics plotter to draw a given figure.