Traveling Salesman Problem -- from Wolfram MathWorld

Traveling Salesman Problem

A problem in graph theory requiring the most efficient (i.e., least total distance) Hamiltonian circuit a salesman can take through each of cities. No general method of solution is known, and the problem is NP-hard. Solution to the traveling salesman problem is implemented as TravelingSalesman[g] in the Mathematica package Combinatorica` (which can be loaded with the command <<Combinatorica`) and FindShortestTour[v1, v2, ...].

The traveling salesman problem is mentioned by the character Larry Fleinhardt in the Season 2 episode "Rampage" (2006) of the television crime drama NUMB3RS.

REFERENCES:

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Reinelt, G. "TSPLIB--A Traveling Salesman Problem Library." ORSA J. Comput. 3, 376-384, 1991.

Rosenkrantz, D. J.; Stearns, R. E.; and Lewis, P. M. "An Analysis of Several Heuristics for the Traveling Salesman Problem." SIAM J. Comput. 6, 563-581, 1977.

Skiena, S. "Traveling Salesman Tours." §5.3.5 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 199-202, 1990.

Skiena, S. S. "Traveling Salesman Problem." §8.5.4 in The Algorithm Design Manual. New York: Springer-Verlag, pp. 319-322, 1997.

Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 120-121, 1999.

CITE THIS AS:

Weisstein, Eric W. "Traveling Salesman Problem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/TravelingSalesmanProblem.html