Princeton, N.J. : Princeton University Press, c2012.
Format:
Book
xiii, 228 p. : ill. (chiefly col.), col. maps ; 24 cm.
Bibliography:
Includes bibliographical references (p. [223]-224) and index.
Contents:
1. Challenges
Tour of the United States
An impossible task?
One problem at a time
Road map of the book
2. Origins of the problem
Before the mathematicians
Euler and Hamilton
Vienna to Harvard to Princeton
And on to the RAND Corporation
A statistical view
3. The salesman in action
Road trips
Mapping genomes
Aiming telescopes, x-rays, and lasers
Guiding industrial machines
Organizing data
Tests for microprocessors
Scheduling jobs
And more
4. Searching for a tour
The 48-states problem
Growing trees and tours
Alterations while you wait
Borrowing from physics and biology
The DIMACS challenge
Tour champions
5. Linear programming
General-purpose model
The simplex algorithm
Two for the price of one: LP duality
The degree LP relaxation of the TSP
Eliminating subtours
A perfect relaxation
Integer programming
Operations research
6. Cutting planes
The cutting-plane method
A catalog of TSP inequalities
The separation problem
Edmonds's glimpse of heaven
Cutting planes for integer programming
7. Branching
Breaking up
The search party
Branch-and-bound for integer programming
8. Big computing
World records
The TSP on a grand scale
9. Complexity
A model of computation
The campaign of Jack Edmonds
Cook's theorem and Karp's list
State of the TSP
Do we need computers?
10. The human touch
Humans versus computers
Tour-finding strategies
The TSP in neuroscience
Animals solving the TSP
Aesthetics
Julian Lethbridge
Jordan curves
Continuous lines
Art and mathematics
Pushing the limits.
Summary:
"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"--Provided by publisher.
"In Pursuit of the Traveling Salesman covers the history, applications, theory, and computation of the traveling salesman problem right up to state-of-the-art solution machinery"--Provided by publisher.