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Tight FPT Approximations for k-Median and k-Means

Authors Vincent Cohen-Addad, Anupam Gupta, Amit Kumar, Euiwoong Lee, Jason Li

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ACM Subject Classification
  • Theory of computation → Facility location and clustering
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → Submodular optimization and polymatroids
Keywords
  • approximation algorithms
  • fixed-parameter tractability
  • k-median
  • k-means
  • clustering
  • core-sets

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Abstract

We investigate the fine-grained complexity of approximating the classical k-Median/k-Means clustering problems in general metric spaces. We show how to improve the approximation factors to (1+2/e+epsilon) and (1+8/e+epsilon) respectively, using algorithms that run in fixed-parameter time. Moreover, we show that we cannot do better in FPT time, modulo recent complexity-theoretic conjectures.

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Vincent Cohen-Addad, Anupam Gupta, Amit Kumar, Euiwoong Lee, and Jason Li. Tight FPT Approximations for k-Median and k-Means. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 42:1-42:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ICALP.2019.42

Author Details

Vincent Cohen-Addad
  • CNRS & Sorbonne Université, Paris, France
Anupam Gupta
  • Carnegie Mellon University, Pittsburgh, PA, USA
Amit Kumar
  • IIT Delhi, India
Euiwoong Lee
  • New York University, NY, USA
Jason Li
  • Carnegie Mellon University, Pittsburgh, PA, USA

Funding

  • Cohen-Addad, Vincent: Ce projet a bénéficié d'une aide de l'Etat gérée par l'Agence Nationale de la Recherche au titre du Programme Appel à projets générique JCJC 2018 portant la référence suivante: ANR-18-CE40-0004-01.
  • Gupta, Anupam: Supported in part by NSF awards CCF-1536002, CCF-1540541, and CCF-1617790.
  • Lee, Euiwoong: Supported in part by the Simons Collaboration on Algorithms and Geometry.
  • Li, Jason: Supported in part by NSF awards CCF-1536002, CCF-1540541, and CCF-1617790.

Acknowledgements

We thank Deeparnab Chakrabarty, Ola Svensson, and Pasin Manurangsi for useful discussions. This research was partially conducted when A. Kumar was visiting A. Gupta and Carnegie Mellon University as part of the Joint Indo-US Virtual Center for Algorithms under Uncertainty.

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