Travelling on Graphs with Small Highway Dimension

We study the Travelling Salesperson (TSP) and Steiner Tree problem (STP) in graphs of low highway dimension. This graph parameter roughly measures how many central nodes are visited by all shortest paths a certain length. It has been shown that transportation networks, on which TSP STP naturally occur for various applications logistics, typically have small While it was previously these problems admit quasi-polynomial time approximation scheme constant dimension, we demonstrate significant improvement is possible special case when dimension 1. Specifically, present fully-polynomial (FPTAS). also prove both weakly $${\mathsf {NP}}$$ -hard restricted graphs.