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

Overview

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 ...

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

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Overview

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. He also explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets.

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.

Some images inside the book are unavailable due to digital copyright restrictions.

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Editorial Reviews

Wall Street Journal
The Traveling Salesman Problem, or TSP, might seem to be of purely recreational interest . . . but in fact, as William J. Cook's In Pursuit of the Traveling Salesman ably shows, the problem remains a topic of hot interest. . . . [This book is] an excellent place for an interested amateur to get the gist of these big ideas in a down-to-earth discussion. . . . 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
New York Journal of Books
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
American Scientist
Along with a heady dose of algorithms, Cook also offers a diverting survey of the lore and history of the TSP. . . . The new volume addresses a wider audience [than The Traveling Salesman Problem: A Computational Study], with more pictures and fewer equations, explaining how things are done rather than how to do them, but it covers all the same territory as the larger book. The path through that territory seems reasonably close to optimal.
— Brian Hayes
hael Trick's Operations Research 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.
Loci: Convergence
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
Math Less Traveled
In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation, does a wonderful job presenting the history and significance of the TSP and an overview of cutting-edge research. It's a beautiful, visually rich book, full of color photographs and diagrams that enliven both the narrative and mathematical presentation. And it includes a wealth of information.
Choice
This book introduces the TSP, its applications, and computational methods for its solution to a general audience.
Loci: Convergence

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
Michael Trick's Operations Research 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.
Business Today Egypt
Cook is spot-on in his delivery of what could be considered by most as an arcane mathematical problem to be solved by only those in the engineering world but like Hawking, peaks interest in a field in which lowly MIT professors could only dream. . . . His witty commentary complements his own casual insertion into the mathematical world and drive to solve the greatest of mathematics' problems. This book is proof that good science writing and mathematics add up.
— Robert Terpstra
Wall Street Journal - Jordan Ellenberg
The Traveling Salesman Problem, or TSP, might seem to be of purely recreational interest . . . but in fact, as William J. Cook's In Pursuit of the Traveling Salesman ably shows, the problem remains a topic of hot interest. . . . [This book is] an excellent place for an interested amateur to get the gist of these big ideas in a down-to-earth discussion. . . . 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.
New York Journal of Books - Robert Schaefer
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.
American Scientist - Brian Hayes
Along with a heady dose of algorithms, Cook also offers a diverting survey of the lore and history of the TSP. . . . The new volume addresses a wider audience [than The Traveling Salesman Problem: A Computational Study], with more pictures and fewer equations, explaining how things are done rather than how to do them, but it covers all the same territory as the larger book. The path through that territory seems reasonably close to optimal.
Loci: Convergence - Christopher Thompson
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.
Business Today Egypt - Robert Terpstra
Cook is spot-on in his delivery of what could be considered by most as an arcane mathematical problem to be solved by only those in the engineering world but like Hawking, peaks interest in a field in which lowly MIT professors could only dream. . . . His witty commentary complements his own casual insertion into the mathematical world and drive to solve the greatest of mathematics' problems. This book is proof that good science writing and mathematics add up.
European Mathematical Society - Gregorio Tirado Dominguez
The technical details are described with precision, but the inherent mathematical concepts are explained in an informal way so that readers without a deep mathematical background can also follow the story. . . . The book is full of examples, real applications and historical anecdotes, making it really enjoyable to read.
ACM SIGACT News - Haris Aziz
The book is highly recommended to any one with a mathematical curiosity and interest in the development of ideas.
Wordplay blog at "New York Times deep Mutalik

Fascinating . . . describes the history, personalities, challenges, applications and techniques used to find solutions of the famous 'Traveling Salesman Problem' and related problems.
Cut the Knot Insights blog xander Bogomolny

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.
European Mathematical Society - Gregorio Tirado Domínguez
The technical details are described with precision, but the inherent mathematical concepts are explained in an informal way so that readers without a deep mathematical background can also follow the story. . . . The book is full of examples, real applications and historical anecdotes, making it really enjoyable to read.
INFORMS Journal on Computing - Gabor Pataki
[T]here is sufficient mathematical detail to provide a good start to readers interested in a more technical treatment. The style is congenial, breezy, and entertaining; many anecdotes and pop culture references are included. Even seasoned researchers will find the book a truly enjoyable read, and it can serve as an ideal basis for a college level freshman seminar.
Mathematics Teacher - S. Leigh Nataro
The author has a solid understanding of the material and tries to present it in an accessible and sometimes entertaining way. . . . I recommend it to anyone interested in gaining a deeper understanding of the TSP and modern developments in solving TSP-like problems.
From the Publisher
"Fascinating . . . describes the history, personalities, challenges, applications and techniques used to find solutions of the famous 'Traveling Salesman Problem' and related problems."—Pradeep Mutalik, Wordplay blog at New York Times

"The Traveling Salesman Problem, or TSP, might seem to be of purely recreational interest . . . but in fact, as William J. Cook's In Pursuit of the Traveling Salesman ably shows, the problem remains a topic of hot interest. . . . [This book is] an excellent place for an interested amateur to get the gist of these big ideas in a down-to-earth discussion. . . . 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, Wall Street Journal

"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

"Along with a heady dose of algorithms, Cook also offers a diverting survey of the lore and history of the TSP. . . . The new volume addresses a wider audience [than The Traveling Salesman Problem: A Computational Study], with more pictures and fewer equations, explaining how things are done rather than how to do them, but it covers all the same territory as the larger book. The path through that territory seems reasonably close to optimal."—Brian Hayes, American Scientist

"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."—Alexander 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."—Michael 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

"In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation, does a wonderful job presenting the history and significance of the TSP and an overview of cutting-edge research. It's a beautiful, visually rich book, full of color photographs and diagrams that enliven both the narrative and mathematical presentation. And it includes a wealth of information."—Math Less Traveled

"This book introduces the TSP, its applications, and computational methods for its solution to a general audience."—Choice

"Cook is spot-on in his delivery of what could be considered by most as an arcane mathematical problem to be solved by only those in the engineering world but like Hawking, peaks interest in a field in which lowly MIT professors could only dream. . . . His witty commentary complements his own casual insertion into the mathematical world and drive to solve the greatest of mathematics' problems. This book is proof that good science writing and mathematics add up."—Robert Terpstra, Business Today Egypt
"The technical details are described with precision, but the inherent mathematical concepts are explained in an informal way so that readers without a deep mathematical background can also follow the story. . . . The book is full of examples, real applications and historical anecdotes, making it really enjoyable to read."—Gregorio Tirado Domínguez, European Mathematical Society

"The book is highly recommended to any one with a mathematical curiosity and interest in the development of ideas."—Haris Aziz, ACM SIGACT News

"[T]here is sufficient mathematical detail to provide a good start to readers interested in a more technical treatment. The style is congenial, breezy, and entertaining; many anecdotes and pop culture references are included. Even seasoned researchers will find the book a truly enjoyable read, and it can serve as an ideal basis for a college level freshman seminar."—Gabor Pataki, INFORMS Journal on Computing

"The author has a solid understanding of the material and tries to present it in an accessible and sometimes entertaining way. . . . I recommend it to anyone interested in gaining a deeper understanding of the TSP and modern developments in solving TSP-like problems."—S. Leigh Nataro, Mathematics Teacher

"[T]his book presents the history and significance of the TSP, and provides an overview of this cutting-edge research in a wonderful way. I recommend it to anybody who is interested in a down-to-earth discussion that provides the most current information on the TSP."—Roberto Baldacci, Interfaces

"This book covers all facets of the TSP and ventures into some very deep theory of complexity and computability. It is written for the general mathematician or scientist but would also be useful to the OR specialist. Overall it is entertaining, richly illustrated and well-referenced. It tells us much about general problem solving as well as the TSP."—Francis McGonigal, Mathematics Today

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Product Details

  • ISBN-13: 9781400839599
  • Publisher: Princeton University Press
  • Publication date: 12/27/2011
  • Sold by: Barnes & Noble
  • Format: eBook
  • Edition description: Course Book
  • Pages: 248
  • Sales rank: 843,320
  • File size: 4 MB

Meet the Author

William J. Cook is professor of combinatorics and optimization at the University of Waterloo. He is the coauthor of "The Traveling Salesman Problem: A Computational Study" (Princeton).
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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

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