User:Thore Husfeldt/TSP translated from DE
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The Travelling Salesman problem (TSP) is a problem in combinatorial optimization studied in operations research and theoretical computer science. Given a list of cities and their pairwise distances, the task is to find a shortest possible tour that visits every city exactly once.
The problem was first formulated as a mathematical problem in 1930 and is one of the most intensively studied problems in optimization. It is used as a benchmark for many optimization methods. Even though the problem is computationally difficult, a large number of heuristics and exact methods are known, so that some instances with tens of thousands of cities can be solved.
The TSP has several applications even in its purest formulation, such as planning, logistics, and the manufacture of microchips. Slighlty modified, it appears as a sub-problem in many areas, such as genome sequencing. In these applications, the concept city represents, for example, customers, soldering points, or DNA fragments, and the concept distance represents travelling times or cost, or a similarity measure between DNA fragments. In many applications, additional constraints such as limited resources or time windows make the problem considerably harder.
In the theory of computational complexity, TSP belongs to the class of NP-complete problems. Thus, it is assumed that there is no efficient algorithm for solving TSP problems. Especially, it is plausible that the worst case running time for an algorithm for TSP depends exponentially on the number of cities, so that even some instances with only dozens of cities cannot be solved exactly.