![]() ![]() Threading a middle ground between these too-fast and too-slow running times, and developing a practical system that can find the exact solution of larger instances, raises difficult questions of algorithm engineering, which have sparked the development of "many of the concepts and techniques of combinatorial optimization". The travelling salesman problem asks to find the shortest cyclic tour of a collection of points, in the plane or in more abstract mathematical spaces.īecause the problem is NP-hard, algorithms that take polynomial time are unlikely to be guaranteed to find its optimal solution on the other hand a brute-force search of all permutations would always solve the problem exactly but would take far too long to be usable for all but the smallest problems. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. Cook, published in 2011 by the Princeton University Press, with a paperback reprint in 2014. In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation is a book on the travelling salesman problem, by William J. ![]()
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