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Finding Longest Geometric Tours

In: Gems of Combinatorial Optimization and Graph Algorithms

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  • Sándor P. Fekete

    (Technische Universität Braunschweig, Department Informatik)

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.

Suggested Citation

  • Sándor P. Fekete, 2015. "Finding Longest Geometric Tours," Springer Books, in: Andreas S. Schulz & Martin Skutella & Sebastian Stiller & Dorothea Wagner (ed.), Gems of Combinatorial Optimization and Graph Algorithms, pages 29-36, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-24971-1_3
    DOI: 10.1007/978-3-319-24971-1_3
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