In pursuit of the traveling salesman : mathemathics at the limits of computation

Author

• Cook, William J.

Additional Author(s)

-

Publisher

Princenton, New Jersey: Princeton University Press, 2012

Language

English

ISBN

9780691163529

Series

Subject(s)

• ALGEBRA
• COMPUTATIONAL COMPLEXITY
• MATHEMATICS-GRAPHIC METHODS
• TRAVELING SALESMAN PROBLEM

Notes

. Includes bibliographical references (p. 225-224) . Includes index (p. 225-228)

Abstract

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

Physical Dimension

Number of Page(s)

xiii, 228 p.

Dimension

24 cm.

Other Desc.

ill.

Summary / Review / Table of Content

Challenges. Tour of the United States --
An impossible task? --
One problem at a time --
Road map of the book --
Origins of the problem. Before the mathematicians --
Euler and Hamilton --
Vienna to Harvard to Princeton --
And on to the RAND Corporation --
A statistical view --
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 --
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 --
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 --
Cutting planes. The cutting-plane method --
A catalog of TSP inequalities --
The separation problem --
Edmonds's glimpse of heaven --
Cutting planes for integer programming --
Branching. Breaking up --
The search party --
Branch-and-bound for integer programming --
Big computing. World records --
The TSP on a grand scale --
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? --
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.

Exemplar(s)

#	Accession No.	Call Number	Location	Status
1.	02190/16	511.5 Coo I	Library - 7th Floor	Available