In Pursuit of the Traveling Salesman

The book presents interesting information about TSP in a lucid manner that would appeal to people without a strong algorithmic background.

I had not realised how much of a research topic the TSP (Travelling Salesman Problem) still is. This book gives a nice overview of the history suitable for a lay audience, but this comes at a price. I found I couldn't follow the description any longer once it got to linear and integer programming. I like to be able to sit down and code something myself but the descriptions here just did not contain the level of detail required to do that. (I probably should have realised that before I bought it.)

The news and ideas in this book are missing.It's no good comparison with other examples of nature,and there are too many pages for the content.On the other side, it has a promising topic.

Solving a most important problem!This book is for mathematicians, computer scientists, computer programmers, and geeks in general. If you are not a member of one these groups, then read no further: this book is not for you. But, if you are a member, this may be exactly what you are looking for!The traveling salesman problem (TSP) is probably the single most important real world problem that must solved every day in many different domains. Simply said, it is a problem of trying to find the shortest possible circuit that visits all cities in a salesman area.Sounds easy? Right?Well, this problem is not easy! If n is number of points that must be reached, there are n factorial ([n-1]!) possible paths! For example, if there are 6 points, then there are 120 possible paths. But if there are 7 cities, then there are 5040 paths! This number grows so fast that for reasonable problems, where there are over 100 points such as in a major airline problem, no computer on the face of the earth can find the optimal path by brute force!Some of the domains include: scheduling aircraft by an airline, determining communication lines by a telephone server, determining the drill pattern on a printed circuit board, industrial process planning in a job shop, determining natural gas flow in a network, etc. In most cases, the problem is solved but not optimally or "best" or "least cost" manners. This book is all about trying to solve this problem to find the best possible solution!While it is very mathematical, the book is actually in a style that is very easy to read and understand. The author is a long time researcher of the TSP. He examines the history of trying to solve the TSP ending with his own major contribution, the Concorde program which found the optimal solution of 85,900 points!Well, is the problem solved? I am sorry to say, despite the looks at the problem by thousands of researchers including Nobel Prize winners, the answer is a hard "NO!" The problem is that the TSP is described as a NP Complete problem, one for which if one can find a polynomial time solution algorithm for, one could win the $1,000,000 Clay Millennium Prize for its solution.This book is outstanding! It describes many of the techniques that have been tried to solve the problem and the problems that were found. For anybody trying their hand at the TSP, I would consider this book a primer, a necessary to read book.Good luck, fellow geeks! There is at least a $1,000,000 out there waiting to reward your brilliance!

The problem of finding the shortest route given a list of locations that need to be visited and a map is an old problem that arose out of practical need. The computational complexity of it though is quite extraordinary as the number of potential routes that need to be examined grows exponentially. The innocuous question of finding the best route has led teams of mathematicians and computer scientists to tackle the problem and whether a polynomial time solution to the problem (more or less a solution for which the computable time can be tackled on a reasonable human scale) is a clay millenium prize problem who's solution will gain the winner 1 million USD. In Pursuit of the Traveling Salesman is an overview of the problem and a readable history of some proposed computational solution methods.The book starts with the history of the problem and introduces similar problems in graph theory as a background. It discusses early thoughts about the problem and how it was proposed and who started to think about it, it is interesting to note that focus on it was geographically broad with it being of practical importance for surveying crops in india (by minimizing the officials journeys when sampling crop yields). The book introduces the reader to how the traveling salesman is relevant in practice in order management, circuit board architecture, food delivery, star gazing, and organizing data that needs fast retrieval. Minimizing distances between points is important for many activities, thus the traveling salesman problem has many applications.The author then focuses on solution methods. This is done in a non-mathematical way, though the ideas are mathematical by nature. The author focuses on intuition and brings the reader up to speed with pictures and well chosen intuitive language. The algorithmic ideas are definitely readable and though many subtleties will be missed, the general ideas of techniques are communicated well. The author also introduces the reader to Linear Programming with well chosen examples and the reader gets a basic grasp of quite technical ideas.The primary contents of the book to me are in description of the algorithms that are primarily used for solving problems and their history. But the author also includes a background about complexity, why the problem of P/NP is important and what solving it means. The author also includes some nice artistic examples of the traveling salesman and discusses how human intuition does a good job of coming close to solutions using basic heuristics. I definitely enjoyed reading this and it was the perfect mix of visual example with written description. One comes through it appreciating the subtelty of what seems to be a simple problem, but is anything but. Highly recommended for those interested in some light math.

We've all had the experience of trying to figure out the best driving route for a circuit of a few places, or at least finding the shortest route through all stops when running a few errands in our own city or town. In mathematics, this conundrum is known as the Traveling Salesman Problem, or TSP, and has been attacked by mathematicians for many decades. The TSP and its wider implications are the subject of this book by William Cook, "In Pursuit of the Traveling Salesman."Cook reviews some of the history of the TSP and recalls some of the mathematicians who made progress on it, and some of the different plans of attack for the problem and the limitations of those approaches are noted. The author explains how the TSP applies not just to road trips, and describes some of the other applications of the TSP in areas such as genome mapping; aiming telescopes, X-rays, and lasers; organizing data; industrial uses; computing; and more. Cook also reports the verdict of mathematicians as to whether they believe TSP will ever be fully solved.This book is significantly more challenging for the general reader than most other popular math books that have come out in the last few years--I CLEPped out of college algebra but was lost in some of the places where Cook broke down some of the more rigorous algorithms used to find better solutions to the TSP. However, the book contains ample diagrams and pictures that help the reader absorb a lot of the material, and the sections of the volume that describe the TSP's wider applications to today's technology would be found accessible by a fairly wide audience.