In pursuit of the traveling salesman: mathematics at the limits of computation Cook, William J.
Material type:
TextPublication details: Princeton Princeton University Press 2014Description: xiii, 228 pISBN: - 9780691163529
- 511.352 C6I6
| Item type | Current library | Collection | Call number | Status | Date due | Barcode | Item holds | |
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Book
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Ahmedabad | Non-fiction | 511.352 C6I6 (Browse shelf(Opens below)) | Available | 191130 |
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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
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.
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