A Systematic Review of Approximability Results for Traveling Salesman Problems leveraging the TSP-T3CO Definition Scheme
CoRR(2023)
摘要
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.
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关键词
salesman
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