| Preface | p. xi |
| The Problem | p. 1 |
| Traveling Salesman | p. 1 |
| Other Travelers | p. 5 |
| Geometry | p. 15 |
| Human Solution of the TSP | p. 31 |
| Engine of Discovery | p. 40 |
| Is the TSP Hard? | p. 44 |
| Milestones in TSP Computation | p. 50 |
| Outline of the Book | p. 56 |
| Applications | p. 59 |
| Logistics | p. 59 |
| Genome Sequencing | p. 63 |
| Scan Chains | p. 67 |
| Drilling Problems | p. 69 |
| Aiming Telescopes and X-Rays | p. 75 |
| Data Clustering | p. 77 |
| Various Applications | p. 78 |
| Dantzig, Fulkerson, and Johnson | p. 81 |
| The 49-City Problem | p. 81 |
| The Cutting-Plane Method | p. 89 |
| Primal Approach | p. 91 |
| History of TSP Computation | p. 93 |
| Branch-and-Bound Method | p. 94 |
| Dynamic Programming | p. 101 |
| Gomory Cuts | p. 102 |
| The Lin-Kernighan Heuristic | p. 103 |
| TSP Cuts | p. 106 |
| Branch-and-Cut Method | p. 117 |
| Notes | p. 125 |
| LP Bounds and Cutting Planes | p. 129 |
| Graphs and Vectors | p. 129 |
| Linear Programming | p. 131 |
| Outline of the Cutting-Plane Method | p. 137 |
| Valid LP Bounds | p. 139 |
| Facet-Inducing Inequalities | p. 142 |
| The Template Paradigm for Finding Cuts | p. 145 |
| Branch-and-Cut Method | p. 148 |
| Hypergraph Inequalities | p. 151 |
| Safe Shrinking | p. 153 |
| Alternative Calls to Separation Routines | p. 156 |
| Subtour Cuts and PQ-Trees | p. 159 |
| Parametric Connectivity | p. 159 |
| Shrinking Heuristic | p. 164 |
| Subtour Cuts from Tour Intervals | p. 164 |
| Padberg-Rinaldi Exact Separation Procedure | p. 170 |
| Storing Tight Sets in PQ-trees | p. 173 |
| Cuts from Blossoms and Blocks | p. 185 |
| Fast Blossoms | p. 185 |
| Blocks of G | p. 1/2 |
| Exact Separation of Blossoms | p. 191 |
| Shrinking | p. 194 |
| Combs from Consecutive Ones | p. 199 |
| Implementation of Phase 2 | p. 202 |
| Proof of the Consecutive Ones Theorem | p. 210 |
| Combs from Dominoes | p. 221 |
| Pulling Teeth from PQ-trees | p. 223 |
| Nonrepresentable Solutions also Yield Cuts | p. 229 |
| Domino-Parity Inequalities | p. 231 |
| Cut Metamorphoses | p. 241 |
| Tighten | p. 243 |
| Teething | p. 248 |
| Naddef-Thienel Separation Algorithms | p. 256 |
| Gluing | p. 261 |
| Local Cuts | p. 271 |
| An Overview | p. 271 |
| Making Choices of V and sigma; | p. 272 |
| Revisionist Policies | p. 274 |
| Does phi;(chi;*) Lie Outside the Convex Hull ofT? | p. 275 |
| Separating phi;(chi;*) fromT: The Three Phases | p. 289 |
| PHASE 1: FromT* toT" | p. 291 |
| PHASE 2: FromT" toT' | p. 315 |
| Implementing ORACLE | p. 326 |
| PHASE 3: FromT' toT | p. 329 |
| Generalizations | p. 339 |
| Managing the Linear Programming Problems | p. 345 |
| The Core LP | p. 345 |
| Cut Storage | p. 354 |
| Edge Pricing | p. 362 |
| The Mechanics | p. 367 |
| The Linear Programming Solver | p. 373 |
| History | p. 373 |
| The Primal Simplex Algorithm | p. 378 |
| The Dual Simplex Algorithm | p. 384 |
| Computational Results: The LP Test Sets | p. 390 |
| Pricing | p. 404 |
| Branching | p. 411 |
| Previous Work | p. 411 |
| Implementing Branch and Cut | p. 413 |
| Strong Branching | p. 415 |
| Tentative Branching | p. 417 |
| Tour Finding | p. 425 |
| Lin-Kernighan | p. 425 |
| Flipper Routines | p. 436 |
| Engineering Lin-Kernighan | p. 449 |
| Chained Lin-Kernighan on TSPLIB Instances | p. 458 |
| Helsgaun's LKH Algorithm | p. 466 |
| Tour Merging | p. 469 |
| Computation | p. 489 |
| The Concorde Code | p. 489 |
| Random Euclidean Instances | p. 493 |
| The TSPLIB | p. 500 |
| Very Large Instances | p. 506 |
| The World TSP | p. 524 |
| The Road Goes On | p. 531 |
| Cutting Planes | p. 531 |
| Tour Heuristics | p. 534 |
| Decomposition Methods | p. 539 |
| Bibliography | p. 541 |
| Index | p. 583 |
| Table of Contents provided by Publisher. All Rights Reserved. |