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The traveling salesman (or salesperson) problem, short TSP, is a problem ofstrong interest to many researchers from mathematics, economics, and computerscience. Manifold TSP variants occur in nearly every scientific field andapplication domain: engineering, physics, biology, life sciences, andmanufacturing just to name a few. Several thousand papers are published ontheoretical research or application-oriented results each year. This paperprovides the first systematic survey on the best currently knownapproximability and inapproximability results for well-known TSP variants suchas the "standard" TSP, Path TSP, Bottleneck TSP, Maximum Scatter TSP,Generalized TSP, Clustered TSP, Traveling Purchaser Problem, Profitable TourProblem, Quota TSP, Prize-Collecting TSP, Orienteering Problem, Time-dependentTSP, TSP with Time Windows, and the Orienteering Problem with Time Windows. Thefoundation of our survey is the definition scheme T3CO, which we propose as auniform, easy-to-use and extensible means for the formal and precise definitionof TSP variants. Applying T3CO to formally define the variant studied by apaper reveals subtle differences within the same named variant and also bringsout the differences between the variants more clearly. We achieve the firstcomprehensive, concise, and compact representation of approximability resultsby using T3CO definitions. This makes it easier to understand theapproximability landscape and the assumptions under which certain results hold.Open gaps become more evident and results can be compared more easily.

A Systematic Review of Approximability Results for Traveling Salesman Problems leveraging the TSP-T3CO Definition Scheme