Cook W.J. In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation

Princeton: Princeton University Press, 2012. — 245 p.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.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.
AlterationsWhile 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.
Notes.