TOPICS

# Traveling Salesman Problem

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 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 if it returns a list with first element equal to the vertex count of .

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

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

## Explore with Wolfram|Alpha

More things to try:

## 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