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The Maximum Scatter TSP on a Regular Grid

In: Operations Research Proceedings 2015

Author

Listed:
  • Isabella Hoffmann

    (Universität Bayreuth)

  • Sascha Kurz

    (Universität Bayreuth)

  • Jörg Rambau

    (Universität Bayreuth)

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.

Suggested Citation

  • Isabella Hoffmann & Sascha Kurz & Jörg Rambau, 2017. "The Maximum Scatter TSP on a Regular Grid," Operations Research Proceedings, in: Karl Franz Dörner & Ivana Ljubic & Georg Pflug & Gernot Tragler (ed.), Operations Research Proceedings 2015, pages 63-70, Springer.
    • Handle: RePEc:spr:oprchp:978-3-319-42902-1_9
    DOI: 10.1007/978-3-319-42902-1_9
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