Input |
Output |

**Input Description:** A weighted graph \(G\). **Problem:** Find the cycle of minimum cost visiting all of the vertices of \(G\) exactly once.

**Excerpt from** The Algorithm Design Manual: The traveling salesman problem is the most notorious NP-complete problem. This is a function of its general usefulness, and because it is easy to explain to the public at large. Imagine a traveling salesman who has to visit each of a given set of cities by car.

Although the problem arises in transportation applications, its most important applications arise in optimizing the tool paths for manufacturing equipment. For example, consider a robot arm assigned to solder all the connections on a printed circuit board. The shortest tour that visits each solder point exactly once defines the most efficient path for the robot. A similar application arises in minimizing the amount of time taken by a graphics plotter to draw a given figure.

Concorde (rating 10) |
TSP solvers (rating 9) |

GOBLIN (rating 9) |
Keld Helsgaun's traveling salesman (rating 8) |

GeneticAlgorithm-TSP (rating 6) |
tsp-solver (rating 6) |

JGraphT (rating 5) |
Netlib (rating 4) |

The Traveling Salesman Problem and Its Variations by G. Gutin and A. Punnen | The Traveling Salesman Problem : A Guided Tour of Combinatorial Optimization by E.L. Lawler (Editor) and A. H. Rinnooy-Kan |

Convex Hull |
Hamiltonian Cycle |
Minimum Spanning Tree |

Satisfiability |

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