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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 Cover

 

Synopses & Reviews

Publisher Comments:

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.

Review:

"But Mr. Cook's affable style means that you're never too far from an enjoyable historical anecdote or an offbeat application of a problem that has interested some of the best minds in applied math for most of a century and that shows no signs of getting stale." --Jordan Ellenberg, The Wall Street Journal

Review:

"...In Pursuit of the Traveling Salesman celebrates all the idiosyncrasies of this particular problem and emphasizes how much progress has been made in solving instances of practical interest, despite the gloomy theoretical outlook. He is personally responsible for a big chunk of that progress." ---Brian Hayes, American Scientist

Synopsis:

"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

Synopsis:

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.

About the Author

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).

Table of Contents

Preface xi

Chapter 1: Challenges 1
Tour of the United States 2
An Impossible Task? 6
One Problem at a Time 10
Road Map of the Book 16

Chapter 2: Origins of the Problem 19
Before the Mathematicians 19
Euler and Hamilton 27
Vienna to Harvard to Princeton 35
And on to the RAND Corporation 38
A Statistical View 39

Chapter 3: The Salesman in Action 44
Road Trips 44
Mapping Genomes 49
Aiming Telescopes, X-rays, and Lasers 51
Guiding Industrial Machines 53
Organizing Data 56
Tests for Microprocessors 59
Scheduling Jobs 60
And More 60

Chapter 4: Searching for a Tour 62
The 48-States Problem 62
Growing Trees and Tours 65
AlterationsWhile You Wait 75
Borrowing from Physics and Biology 84
The DIMACS Challenge 91
Tour Champions 92

Chapter 5: Linear Programming 94
General-Purpose Model 94
The Simplex Algorithm 99
Two for the Price of One: LP Duality 105
The Degree LP Relaxation of the TSP 108
Eliminating Subtours 113
A Perfect Relaxation 118
Integer Programming 122
Operations Research 125

Chapter 6: Cutting Planes 127
The Cutting-Plane Method 127
A Catalog of TSP Inequalities 131
The Separation Problem 137
Edmonds's Glimpse of Heaven 142
Cutting Planes for Integer Programming 144

Chapter 7: Branching 146
Breaking Up 146
The Search Party 148
Branch-and-bound for Integer Programming 151

Chapter 8: Big Computing 153
World Records 153
The TSP on a Grand Scale 163

Chapter 9: Complexity 168
A Model of Computation 169
The Campaign of Jack Edmonds 171
Cook's Theorem and Karp's List 174
State of the TSP 178
Do We Need Computers? 184

Chapter 10: The Human Touch 191
Humans versus Computers 191
Tour-finding Strategies 192
The TSP in Neuroscience 196
Animals Solving the TSP 197

Chapter 11: Aesthetics 199
Julian Lethbridge 199
Jordan Curves 201
Continuous Lines 205
Art and Mathematics 207
Chapter 12: Pushing the Limits 211

Notes 213
Bibliography 223
Index 225

Product Details

ISBN:
9780691152707
Author:
Cook, William J.
Publisher:
Princeton University Press
Subject:
General Mathematics
Subject:
Mathematics
Subject:
History of Science and Medicine, Philosophy of Science
Subject:
Mathematics-Games and Puzzles
Subject:
Mathematics - General
Subject:
Popular science
Subject:
Mathematics -- History.
Subject:
Computer Science
Copyright:
Publication Date:
20120116
Binding:
HARDCOVER
Language:
English
Illustrations:
113 color illus. 19 halftones. 19 line i
Pages:
272
Dimensions:
9 x 6 in

Related Subjects

Reference » Science Reference » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » History
Science and Mathematics » Mathematics » Popular Surveys and Recreational

In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation New Hardcover
0 stars - 0 reviews
$27.95 In Stock
Product details 272 pages Princeton University Press - English 9780691152707 Reviews:
"Review" by , "But Mr. Cook's affable style means that you're never too far from an enjoyable historical anecdote or an offbeat application of a problem that has interested some of the best minds in applied math for most of a century and that shows no signs of getting stale." --
"Review" by , "...In Pursuit of the Traveling Salesman celebrates all the idiosyncrasies of this particular problem and emphasizes how much progress has been made in solving instances of practical interest, despite the gloomy theoretical outlook. He is personally responsible for a big chunk of that progress." ---
"Synopsis" by , "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

"Synopsis" by , 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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