This book presents the latest findings on one of the most intensely investigated subjects in computational mathematics--the traveling salesman problem. It sounds simple enough: given a set of cities and the cost of travel between each pair of them, the problem challenges you to find the cheapest route by which to visit all the cities and return home to where you began. Though seemingly modest, this exercise has inspired studies by mathematicians, chemists, and physicists. Teachers use it in the classroom. It has practical applications in genetics, telecommunications, and neuroscience.
The authors of this book are the same pioneers who for nearly two decades have led the investigation into the traveling salesman problem. They have derived solutions to almost eighty-six thousand cities, yet a general solution to the problem has yet to be discovered. Here they describe the method and computer code they used to solve a broad range of large-scale problems, and along the way they demonstrate the interplay of applied mathematics with increasingly powerful computing platforms. They also give the fascinating history of the problem--how it developed, and why it continues to intrigue us.

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Yes, you can access Princeton Series in Applied Mathematics by David L. Applegate,Robert E. Bixby,Vašek Chvátal,William J. Cook in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.

Information

Publisher

Princeton University Press

Year

2011

ISBN

9781400841103

Topic

Mathematics

Subtopic

Applied Mathematics

Index

Mathematics

Cover
Half title
Title
Copyright
Dedication
Contents
Preface
Chapter 1. The Problem
Chapter 2. Applications
Chapter 3. Dantzig, Fulkerson, and Johnson
Chapter 4. History of TSP Computation
Chapter 5. LP Bounds and Cutting Planes
Chapter 6. Subtour Cuts and PQ-Trees
Chapter 7. Cuts from Blossoms and Blocks
Chapter 8. Combs from Consecutive Ones
Chapter 9. Combs from Dominoes
Chapter 10. Cut Metamorphoses
Chapter 11. Local Cuts
Chapter 12. Managing the Linear Programming Problems
Chapter 13. The Linear Programming Solver
Chapter 14. Branching
Chapter 15. Tour Finding
Chapter 16. Computation
Chapter 17. The Road Goes On
Bibliography
Index