Abstract
In this paper we introduce and study cooperative variants of the Traveling Salesperson Problem. In these problems a salesperson has to make deliveries to customers who are willing to help in the process. Customer cooperativeness may be manifested in several modes: they may assist by approaching the salesperson, by reselling the goods they purchased to other customers, or by doing both.
Several objectives are of interest: minimizing the total distance traveled by all the participants, minimizing the maximal distance traveled by a participant and minimizing the total time until all the deliveries are made.
All the combinations of cooperation-modes and objective functions are considered, both in weighted undirected graphs and in Euclidean space. We show that most of the problems have a constant approximation algorithm, many of the others admit a PTAS, and a few are solvable in polynomial time. On the intractability side we provide NP-hardness proofs and inapproximability factors, some of which are tight.
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Armon, A., Avidor, A., Schwartz, O. (2006). Cooperative TSP. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_7
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DOI: https://doi.org/10.1007/11841036_7
Publisher Name: Springer, Berlin, Heidelberg
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