Abstract
In the Maximum Scatter Traveling Salesman Problem the objective is to find a tour that maximizes the shortest distance between any two consecutive nodes. This model can be applied to manufacturing processes, particularly laser melting processes. We extend an algorithm by Arkin et al. that yields optimal solutions for nodes on a line to a regular (\(m \times n\))-grid. The new algorithm \(\textsc {Weave}(m,n)\) takes linear time to compute an optimal tour in some cases. It is asymptotically optimal and a (\(\frac{\sqrt{10}}{5}\))-approximation for the (\(3\times 4\))-grid, which is the worst case.
I. Hoffmann Partially supported by a grant of the Oberfrankenstiftung, project number: 03549.
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References
Arkin, E., Chiang, Y.-J., Mitchell, J.S.B., Skiena, S.S., Yang, T.-C.: On the maximum scatter TSP. SIAM J. Comput. 29, 515–544 (1999)
Chiang, Y.-J.: New approximation results for the maximum scatter TSP. Algorithmica 41, 309–341 (2005)
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Hoffmann, I., Kurz, S., Rambau, J. (2017). The Maximum Scatter TSP on a Regular Grid. In: Dörner, K., Ljubic, I., Pflug, G., Tragler, G. (eds) Operations Research Proceedings 2015. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-42902-1_9
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DOI: https://doi.org/10.1007/978-3-319-42902-1_9
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