Cook In Pursuit of the Traveling Salesman

Mathematics at the Limits of Computation
Course Book
ISBN: 978-1-4008-3959-9
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 248 Seiten

No detailed description available for "In Pursuit of the Traveling Salesman".

Autoren/Hrsg.

Cook, William J.

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Mathematik | Informatik EDV | Informatik Informatik Theoretische Informatik
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Inhaltsverzeichnis

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

Über Autor(innen)

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).