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Conference Papers Year : 2020

Polynomial Time Approximation Schemes for Clustering in Low Highway Dimension Graphs

Andreas Emil Feldmann
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David Saulpic

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 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.
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hal-02980463 , version 1 (27-10-2020)

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Andreas Emil Feldmann, David Saulpic. Polynomial Time Approximation Schemes for Clustering in Low Highway Dimension Graphs. 28th Annual European Symposium on Algorithms (ESA 2020), Sep 2020, Pisa, Italy. pp.46:1--46:22, ⟨10.4230/LIPIcs.ESA.2020.46⟩. ⟨hal-02980463⟩
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