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

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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
Publication Date:
20120131
Binding:
HARDCOVER
Language:
English
Illustrations:
113 color illus. 19 halftones. 19 line i
Pages:
248
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 248 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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