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Traveling Salesman Problem


TravelingSalesmanProblem

The traveling salesman problem is a problem in graph theory requiring the most efficient (i.e., least total distance) Hamiltonian cycle a salesman can take through each of n cities. No general method of solution is known, and the problem is NP-hard.

The Wolfram Language command FindShortestTour[g] attempts to find a shortest tour, which is a Hamiltonian cycle (with initial vertex repeated at the end) for a Hamiltonian graph G if it returns a list with first element equal to the vertex count of G.

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


See also

Ant Colony Algorithm, Chinese Postman Problem, Dendrite, Hamiltonian Cycle, Longest Path, Optimization, Plateau's Problem, Road Coloring Problem, Traveling Salesman Constants

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References

Applegate, D.; Bixby, R.; Chvatal, V.; and Cook, W. "Finding Cuts in the TSP (a Preliminary Report)." Technical Report 95-05, DIMACS. Piscataway NJ: Rutgers University, 1995.Applegate, D.; Bixby, R.; Chvatal, V.; and Cook, W. "Solving Traveling Salesman Problems." http://www.tsp.gatech.edu/.Hoffman, P. The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. New York: Hyperion, pp. 168-169, 1998.Kruskal, J. B. "On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem." Proc. Amer. Math. Soc. 7, 48-50, 1956.Lawler, E.; Lenstra, J.; Rinnooy Kan, A.; and Shmoys, D. The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. New York: Wiley, 1985.Lin, S. "Computer Solutions of the Traveling Salesman Problem." Bell System Tech. J. 44, 2245-2269, 1965.Platzman, L. K. and Bartholdi, J. J. "Spacefilling Curves and the Planar Travelling Salesman Problem." J. Assoc. Comput. Mach. 46, 719-737, 1989.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. https://mathworld.wolfram.com/TravelingSalesmanProblem.html

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