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arXiv · 1902.07040

Travelling on Graphs with Small Highway Dimension

Yann Disser·Andreas Emil Feldmann·Max Klimm·Jochen Konemann
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Abstract

We study the Travelling Salesperson (TSP) and the Steiner Tree problem (STP) in graphs of low highway dimension. This graph parameter was introduced by Abraham et al. [SODA 2010] as a model for transportation networks, on which TSP and STP naturally occur for various applications in logistics. It was previously shown [Feldmann et al. ICALP 2015] that these problems admit a quasi-polynomial time approximation scheme (QPTAS) on graphs of constant highway dimension. We demonstrate that a significant improvement is possible in the special case when the highway dimension is 1, for which we present a fully-polynomial time approximation scheme (FPTAS). We also prove that STP is weakly NP-hard for these restricted graphs. For TSP we show NP-hardness for graphs of highway dimension 6, which answers an open problem posed in [Feldmann et al. ICALP 2015].

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Yann Disser, Andreas Emil Feldmann, Max Klimm, Jochen Konemann. 2019-02-19. Travelling on Graphs with Small Highway Dimension. https://arxiv.org/abs/1902.07040

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