Polynomial Time Approximation Schemes for Clustering in Low Highway Dimension Graphs

Andreas Emil Feldmann, David Saulpic, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
We study clustering problems such as k-Median, k-Means, and Facility Location in graphs of low highway dimension, which is a graph parameter modeling transportation networks. It was previously shown that approximation schemes for these problems exist, which either run in quasi-polynomial time (assuming constant highway dimension) [Feldmann et al. SICOMP 2018] or run in FPT time (parameterized by the number of clusters k, the highway dimension, and the approximation factor) [Becker et al. ESA
more » ... 8, Braverman et al. 2020]. In this paper we show that a polynomial-time approximation scheme (PTAS) exists (assuming constant highway dimension). We also show that the considered problems are NP-hard on graphs of highway dimension 1.
doi:10.4230/lipics.esa.2020.46 dblp:conf/esa/FeldmannS20 fatcat:ttpadxqgpfahnd4cxbvodb7cmu