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

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, 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 ap, 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
  • Written by author William J. Cook
  • Published by Princeton University Press, 1/16/2012
  • 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 ap
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Authors

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

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

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