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Finding Longest Geometric Tours

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Gems of Combinatorial Optimization and Graph Algorithms

Abstract

We discuss the problem of finding a longest tour for a set of points in a geometric space. In particular, we show that a longest tour for a set of n points in the plane can be computed in time O(n) if distances are determined by the Manhattan metric, while the same problem is NP-hard for points on a sphere under Euclidean distances.

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Authors and Affiliations

  1. Department Informatik, Technische Universität Braunschweig, Mühlenpfordtstraße 23, 38106, Braunschweig, Germany

    Sándor P. Fekete

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  1. Sándor P. Fekete
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Correspondence to Sándor P. Fekete .

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Editors and Affiliations

  1. Technische Universität München, Munich, Germany

    Andreas S. Schulz

  2. Institute of Mathematics, Technische Universität Berlin, Berlin, Berlin, Germany

    Martin Skutella

  3. Technische Universität Braunschweig, Braunschweig, Germany

    Sebastian Stiller

  4. Institute of Theoretical Informatics, Karlsruher Institut für Technologie (KIT), Karlsruhe, Germany

    Dorothea Wagner

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Fekete, S.P. (2015). Finding Longest Geometric Tours. In: Schulz, A., Skutella, M., Stiller, S., Wagner, D. (eds) Gems of Combinatorial Optimization and Graph Algorithms . Springer, Cham. https://doi.org/10.1007/978-3-319-24971-1_3

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