The Maximum Scatter TSP on a Regular Grid

Conference paper
Part of the Operations Research Proceedings book series (ORP)

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.

References

  1. 1.
    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)CrossRefGoogle Scholar
  2. 2.
    Chiang, Y.-J.: New approximation results for the maximum scatter TSP. Algorithmica 41, 309–341 (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Universität BayreuthBayreuthGermany

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