Polynomial Time Approximation Schemes for Clustering in Low Highway Dimension Graphs
Data Structures and Algorithms
2021-06-01 v3
Abstract
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 , the highway dimension, and the approximation factor) [Becker et al. ESA~2018, 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.
Cite
@article{arxiv.2006.12897,
title = {Polynomial Time Approximation Schemes for Clustering in Low Highway Dimension Graphs},
author = {Andreas Emil Feldmann and David Saulpic},
journal= {arXiv preprint arXiv:2006.12897},
year = {2021}
}