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。几乎在每个科学领域和应用场景——从工程、物理、生物学、生命科学到制造业——都会出现多种TSP变体。每年有数千篇论文发表关于理论研究成果或应用导向的结果。本文首次系统综述了当前已知最优的近似性与不可近似性结果，涵盖多种经典TSP变体，包括"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、盈利巡游问题、配额TSP、奖励收集TSP、定向越野问题、时变TSP、带时间窗TSP以及带时间窗定向越野问题。本综述的基础是T3CO定义方案，我们将其提出为一种统一、易用且可扩展的框架，用于正式且精确地定义TSP变体。通过应用T3CO对论文所研究变体进行形式化定义，既能揭示同名变体内部的细微差异，也能更清晰地凸显不同变体之间的区别。我们借助T3CO定义首次实现了可近似性结果的全面、简洁且紧凑的表示，从而更便于理解可近似性全貌以及特定结果成立的假设条件，使现存的理论空白更加清晰，结果间的比较也更加便捷。