License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2020.46
URN: urn:nbn:de:0030-drops-129129
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12912/
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Feldmann, Andreas Emil ; Saulpic, David

Polynomial Time Approximation Schemes for Clustering in Low Highway Dimension Graphs

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LIPIcs-ESA-2020-46.pdf (0.6 MB)

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.

BibTeX - Entry

@InProceedings{feldmann_et_al:LIPIcs:2020:12912,
  author =	{Andreas Emil Feldmann and David Saulpic},
  title =	{{Polynomial Time Approximation Schemes for Clustering in Low Highway Dimension Graphs}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{46:1--46:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12912},
  URN =		{urn:nbn:de:0030-drops-129129},
  doi =		{10.4230/LIPIcs.ESA.2020.46},
  annote =	{Keywords: Approximation Scheme, Clustering, Highway Dimension}
}

Keywords: Approximation Scheme, Clustering, Highway Dimension
Collection: 28th Annual European Symposium on Algorithms (ESA 2020)
Issue Date: 2020
Date of publication: 26.08.2020

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