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Travelling Salesman Problem (TSP)

The Travelling Salesman Problem (TSP) is an NP-hard problem.

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The TSP (Travelling Salesman Problem) has several applications, such as planning, logistics, and the manufacture of microchips. Slightly modified, it appears as a sub-problem in many areas, such as DNA sequencing.

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As A Graph Problem

Travelling salesman problem can be modeled as an undirected weighted graph, such that cities are the graph's vertices, paths are the graph's edges, and a path's distance is the edge's length. A TSP tour becomes a Hamiltonian cycle if and only if every edge has the same distance. Often, the model is a complete graph. If no path exists between two cities, adding an arbitrarily long edge will complete the graph without affecting the optimal tour.

Fig: Symmetric TSP with four cities

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