🤖 AI Summary
Existing approximation results for the Traveling Salesman Problem (TSP) and its numerous variants—including Path TSP, Bottleneck TSP, and Generalized TSP—lack systematic organization, standardized definitions, and clarified boundaries, hindering comparability and interpretability.
Method: We introduce TSP-T3CO, the first unified, precise, and extensible formal framework for TSP variants. Leveraging formal modeling, computational complexity analysis, and a comprehensive literature survey, we rigorously define and categorize over two dozen variants, explicitly stating underlying assumptions and approximation guarantees.
Contribution/Results: TSP-T3CO delivers the first compact, assumption-transparent, and cross-variant approximation landscape for TSP. It consolidates and reconciles known approximation ratios and inapproximability bounds, enhances result reproducibility and interpretability, and identifies critical open problems. By establishing a structured, benchmark-quality reference, this work provides a foundational resource for future algorithmic design and theoretical investigation of combinatorial optimization problems rooted in TSP.
📝 Abstract
The traveling salesman (or salesperson) problem, short TSP, is of strong interest to many researchers from mathematics, economics, and computer science. Manifold TSP variants occur in nearly every scientific field and application domain: e.g., engineering, physics, biology, life sciences, and manufacturing. Several thousand papers are published every 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”, Path, Bottleneck, Maximum Scatter, Generalized, Clustered, Quota, Prize-Collecting, Time-dependent TSP, Traveling Purchaser Problem, Profitable Tour Problem, Orienteering Problem, TSP with Time Windows, and Orienteering Problem with Time Windows. The foundation of our survey is the definition scheme TSP-T3CO , which we propose as a uniform, easy-to-use and extensible means for the formal and precise definition of TSP variants. Applying TSP-T3CO to define a TSP variant reveals subtle differences within the same named variant and also brings out the differences between variants more clearly. We achieve the first comprehensive, concise, and compact representation of approximability results by using TSP-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.
