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In Pursuit of the Travelling Salesman: Mathematics at the Limits of Computation by William J Cook

This is one of those maths books that describes the problem, and then tells the story of the various historical approaches to solving it. The story is fascinating, and in the pre-computer days involved massive amounts of hand calculation using clever tricks to prove lower bounds for various instances of the problem.

Along the way we learn about the P!=NP conjecture, and also learn about the simplex method and integer programming which can be used as a way to get strong lower bounds for various for travelling salesman problems (using so called control zones).

A good interesting read.

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