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.

REFERENCES:

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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.

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