The Traveling Salesman Problem: A Computational Study

by David L. Applegate, Robert E. Bixby, Vasek Chvatal

This book presents the latest findings on one of the most intensely investigated subjects in computational mathematics--the traveling salesman problem. It sounds simple given a set of cities and the cost of travel between each pair of them, the problem challenges you to find the cheapest route by which to visit all the cities and return home to where you began. Though seemingly modest, this exercise has inspired studies by mathematicians, chemists, and physicists. Teachers use it in the classroom. It has practical applications in genetics, telecommunications, and neuroscience.


The authors of this book are the same pioneers who for nearly two decades have led the investigation into the traveling salesman problem. They have derived solutions to almost eighty-six thousand cities, yet a general solution to the problem has yet to be discovered. Here they describe the method and computer code they used to solve a broad range of large-scale problems, and along the way they demonstrate the interplay of applied mathematics with increasingly powerful computing platforms. They also give the fascinating history of the problem--how it developed, and why it continues to intrigue us.

Genres: Algorithms

608 pages, Hardcover

First published December 1, 2006

Reviews

[Barry · Rating 5 out of 5]

Given n cities, what is the shortest tour that passes through each city and returns to the place where you started? This is the rare mathematical problem that manages to have real-world relevance, be easily understandable to non-mathematicians, and be difficult enough that a successful solution would net the lucky programmer a million dollar prize from the Clay Mathematics Institute.

There is something very pleasing about a book that focuses so tightly on a single topic and yet requires 540 dense pages to accomplish what amounts to an overview (there are more bibliographic references than pages -- always a good sign).

If you're lucky enough to have the luxury to devote a few hours to some interesting, easily-approachable math, get the book from the library and enjoy the first couple of chapters.

To the intended audience: the book is a bit Concorde-specific, and as the source code for Concorde is not available, this is a bit worrisome. (Gutin's book has a chapter dedicated to software alternatives.) Aside from that, this is the most recent compendium I'm aware of and a very solid piece of work.

[Romerl Elizes · Rating 4 out of 5]

Excellent research companion for my dissertation! Lots of information and guidelines for research outcomes and ideas.

[Devendra Owens · Rating 4 out of 5]

Very good introduction to one of the most famous mathematical problems