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Polynomial Time Approximation Schemes for Clustering in Low Highway Dimension Graphs

Authors Andreas Emil Feldmann , David Saulpic

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Andreas Emil Feldmann
  • Charles University, Prague, Czech Republic
David Saulpic
  • LIP6, Sorbonne Université, Paris, France


We thank Vincent Cohen-Addad for helpful discussions.

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Andreas Emil Feldmann and David Saulpic. Polynomial Time Approximation Schemes for Clustering in Low Highway Dimension Graphs. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 46:1-46:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
  • Approximation Scheme
  • Clustering
  • Highway Dimension


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