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In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation
 
 
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In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation [Hardcover]

William J. Cook (Author)
5.0 out of 5 stars  See all reviews (2 customer reviews)

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Book Description

December 27, 2011

What is the shortest possible route for a traveling salesman seeking to visit each city on a list exactly once and return to his city of origin? It sounds simple enough, yet the traveling salesman problem is one of the most intensely studied puzzles in applied mathematics--and it has defied solution to this day. In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and venturing to the furthest limits of today's state-of-the-art attempts to solve it.

Cook examines the origins and history of the salesman problem and explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets. He looks at how computers stack up against the traveling salesman problem on a grand scale, and discusses how humans, unaided by computers, go about trying to solve the puzzle. Cook traces the salesman problem to the realms of neuroscience, psychology, and art, and he also challenges readers to tackle the problem themselves. The traveling salesman problem is--literally--a $1 million question. That's the prize the Clay Mathematics Institute is offering to anyone who can solve the problem or prove that it can't be done.

In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem.


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Editorial Reviews

Review

Fascinating . . . describes the history, personalities, challenges, applications and techniques used to find solutions of the famous 'Traveling Salesman Problem' and related problems. -- deep Mutalik, Wordplay blog at "New York Times

The author, William Cook, writes in an easy to understand style and explores the various algorithms and branches of mathematics used to solve TSP, including the branch of mathematics known as linear programming, which is known to most of us through grade school algebra and word problems. . . . In Pursuit of the Traveling Salesman is a thoroughly entertaining nerd-fest for the science minded reader. -- Robert Schaefer, New York Journal of Books

In Pursuit of the Traveling Salesman is a first-hand and a first-class introduction into the evolution of TSP, with chapters devoted to related mathematics and algorithmic topics. TSP is really at the heart of much of the research and development of modern computer science, so the author leads the reader through the past and emerging landscape of relevant research up to the very end of the mapped territory. Reading the book looks like an exciting adventure, with the itinerary mapped for the reader by a master story-teller whose work squarely places him in the forefront of the TSP research. -- xander Bogomolny, Cut the Knot Insights blog

Bill takes his readers down a beautiful path covering the history, applications, and algorithms associated with the TSP. It is a fascinating story, and one that shows a researcher who truly loves his research area. . . . Through this book, you'll learn all about the Traveling Salesman Problem and, more broadly, about the different research directions in combinatorial optimization. -- hael Trick's Operations Research Blog

In his new book, aptly titled In Pursuit of the Traveling Salesman, William Cook enlists us to join him on a personal journey through all-things past and present regarding this mammoth of a mathematical problem. . . . I would highly recommend this book to interested readers and high school mathematics teachers, especially those of upper-level coursework. A great deal of mathematics is covered here and the TSP can easily spark debate and inquiry in the classroom. -- Christopher Thompson, Loci: Convergence

From the Inside Flap

"A gripping insider's account of one of the great mathematical problems. This book shows how deep mathematical insights can arise from apparently simple questions, and how the results can be applied to that most human of objectives: to achieve a desired outcome in the best possible way. In Pursuit of the Traveling Salesman deserves to become an instant classic."--Ian Stewart, author of Professor Stewart's Hoard of Mathematical Treasures

"I found this to be a wonderful book on many levels. The writing is informal but precise, and a lot of ground is covered. Cook ties together so many diverse topics and includes informative discussions about the history. I now know a lot more about every aspect of the traveling salesman problem."--Stan Wagon, Macalester College, author of Mathematica in Action

"Cook makes a compelling case for the importance of the traveling salesman problem, revealing that while many brilliant minds have worked on the problem, the next key insight could really come from anyone. Because of his centrality to the research, he writes with a depth of knowledge and experience that few--if any--can surpass. I know of no other book like this."--Mitchel T. Keller, London School of Economics and Political Science


Product Details

  • Hardcover: 272 pages
  • Publisher: Princeton University Press (December 27, 2011)
  • Language: English
  • ISBN-10: 0691152705
  • ISBN-13: 978-0691152707
  • Product Dimensions: 9.3 x 6.2 x 0.9 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #21,323 in Books (See Top 100 in Books)

More About the Author

William Cook is the Chandler Family Professor at Georgia Tech and a member of the National Academy of Engineering. Together with David Applegate, Robert Bixby, and Vasek Chvatal, Cook created the Concorde computer code for the traveling salesman problem.

 

Customer Reviews

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9 of 9 people found the following review helpful:
5.0 out of 5 stars Loving the Traveling Salesman Problem, January 14, 2012
This review is from: In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation (Hardcover)
The Traveling Salesman Problem is remarkable easy to state: given a set of points with distances between them, find the shortest tour through all the points. Despite its simple statement, the problem of finding good or optimal tours has generated thousands of research papers. The TSP is the standard testbed for discrete optimization: practically every possible approach to optimization can be tried out on the TSP. So research on the TSP has had a tremendous effect on approaches for all sorts of other optimization problems. This paper covers every aspect of this research corpus.

The author is the world's expert on this topic, and is clearly enraptured with this problem. His affection shows through his naming of his favorite heuristic, favorite computational model, and more. The book is wide-ranging and thorough and is written in a consistently engaging, conversational style, even when going very deep into the research literature.

This is not a research book, but it is a book about research. Through the TSP, Cook describes how research is done in a wide variety of subfields. The book requires some concentration but is accessible to any mathematically-inclined college student or bright high school student. For many, it will inspire further interest in algorithms and research.
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4 of 5 people found the following review helpful:
5.0 out of 5 stars One of the best recreational math books, January 31, 2012
This review is from: In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation (Hardcover)
I have a few thousand books on recreational mathematics, so it's always fun to find a true gem that is superbly researched, well-illustrated, and well-written. IPotTS:MatLoC is one of those rare books.

When I was a boy, it was a few well-illustrated math books that drew me in. I didn't really understand some of the things in the books, but I wanted to. Then in fifth grade, I was taught about plotting a point, and suddenly the odd graphs in the books made sense.

Various websites such as the Wolfram demonstrations project have dozens of ready-to-run programs dealing with the Traveling Salesman Problem. You have 20 or so cities, and you must plot the ideal route that goes through them all. The authors thorough discuss all the ins and outs of the problem, which is still unsolved. There are many excellent ways to get a really good solution for a given set of 100 random points, but proving that the best solution has been found, by checking all tours, is currently computationally impossible above some number of points.

There is a lot of material in here approachable by anyone. Fun facts, such as a competition for finding the optimal way to drill 318 holes in a circuit board. In the description are the names of the mathematicians and methods, then it's on to the next fun fact. It mentions that the cutting plane algorithm was used, which is wonderfully explained in another chapter.

Highly recommended.

As Marion Harris says in the Left All Alone Again Blues:
No woman knows, if she has a travelin' husband
Just where he goes
Unless she follows on and nails him, trails him ...
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