In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation

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Princeton University Press, 2012 - Mathematics - 228 pages
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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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Contents

1 Challenges
1
2 Origins of the Problem
19
3 The Salesman in Action
44
4 Searching for a Tour
62
5 Linear Programming
94
6 Cutting Planes
127
7 Branching
146
8 Big Computing
153
9 Complexity
168
10 The Human Touch
191
11 Aesthetics
199
12 Pushing the Limits
211
Notes
213
Bibliography
223
Index
225
Copyright

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About the author (2012)

William J. Cook is the Chandler Family Chair and Professor in Industrial and Systems Engineering at Georgia Institute of Technology. He is the coauthor of "The Traveling Salesman Problem: A Computational Study" (Princeton).

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