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In Pursuit of the Traveling Salesman

Book Description

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.

Cook examines the origins and history of the salesman problem and explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets. He looks at how computers stack up against the traveling salesman problem on a grand scale, and discusses how humans, unaided by computers, go about trying to solve the puzzle. Cook traces the salesman problem to the realms of neuroscience, psychology, and art, and he also challenges readers to tackle the problem themselves. The traveling salesman problem is--literally--a $1 million question. That's the prize the Clay Mathematics Institute is offering to anyone who can solve the problem or prove that it can't be done.

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.

Some images inside the book are unavailable due to digital copyright restrictions.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Dedication
  5. Contents
  6. Preface
  7. 1 Challenges
    1. Tour of the United States
    2. An Impossible Task?
    3. One Problem at a Time
    4. Road Map of the Book
  8. 2 Origins of the Problem
    1. Before the Mathematicians
    2. Euler and Hamilton
    3. Vienna to Harvard to Princeton
    4. And on to the RAND Corporation
    5. A Statistical View
  9. 3 The Salesman in Action
    1. Road Trips
    2. Mapping Genomes
    3. Aiming Telescopes, X-rays, and Lasers
    4. Guiding Industrial Machines
    5. Organizing Data
    6. Tests for Microprocessors
    7. Scheduling Jobs
    8. And More
  10. 4 Searching for a Tour
    1. The 48-States Problem
    2. Growing Trees and Tours
    3. Alterations While You Wait
    4. Borrowing from Physics and Biology
    5. The DIMACS Challenge
    6. Tour Champions
  11. 5 Linear Programming
    1. General-Purpose Model
    2. The Simplex Algorithm
    3. Two for the Price of One: LP Duality
    4. The Degree LP Relaxation of the TSP
    5. Eliminating Subtours
    6. A Perfect Relaxation
    7. Integer Programming
    8. Operations Research
  12. 6 Cutting Planes
    1. The Cutting-Plane Method
    2. A Catalog of TSP Inequalities
    3. The Separation Problem
    4. Edmonds’s Glimpse of Heaven
    5. Cutting Planes for Integer Programming
  13. 7 Branching
    1. Breaking Up
    2. The Search Party
    3. Branch-and-bound for Integer Programming
  14. 8 Big Computing
    1. World Records
    2. The TSP on a Grand Scale
  15. 9 Complexity
    1. A Model of Computation
    2. The Campaign of Jack Edmonds
    3. Cook’s Theorem and Karp’s List
    4. State of the TSP
    5. Do We Need Computers?
  16. 10 The Human Touch
    1. Humans versus Computers
    2. Tour-finding Strategies
    3. The TSP in Neuroscience
    4. Animals Solving the TSP
  17. 11 Aesthetics
    1. Julian Lethbridge
    2. Jordan Curves
    3. Continuous Lines
    4. Art and Mathematics
  18. 12 Pushing the Limits
  19. Notes
  20. Bibliography
  21. Index