In Pursuit of the Traveling Salesman

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).

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