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

翻译：旅行商问题（简称TSP）是数学、经济学和计算机科学领域众多研究者高度关注的问题。多种TSP变体几乎出现在所有科学领域和应用场景中：工程学、物理学、生物学、生命科学、制造业等仅是其中数例。每年有数千篇论文发表相关理论研究或应用成果。本文首次系统综述了当前已知的经典TSP变体的最佳近似性与不可近似性结果，涵盖“标准”TSP、路径TSP、瓶颈TSP、最大分散TSP、广义TSP、聚类TSP、旅行采购问题、盈利游历问题、定额TSP、奖金收集TSP、定向问题、时变TSP、带时间窗TSP以及带时间窗定向问题。本综述的基础是T3CO定义框架，我们提出该框架作为统一、易用且可扩展的形式化精确定义TSP变体的工具。运用T3CO形式化定义论文研究的变体，能够揭示同名变体间的细微差异，并更清晰地凸显不同变体间的区别。通过采用T3CO定义，我们首次实现了近似性结果的全面、简明且紧凑的呈现。这有助于理解近似性研究的整体格局及特定结果成立的前提条件，使研究空白更明显，结果对比更便捷。