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Clustering with Faulty Centers

Authors Kyle Fox, Hongyao Huang, Benjamin Raichel

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Author Details

Kyle Fox
  • University of Texas at Dallas, TX, USA
Hongyao Huang
  • University of Texas at Dallas, TX, USA
Benjamin Raichel
  • University of Texas at Dallas, TX, USA

Funding

  • Fox, Kyle: Research partially supported by NSF grant CCF-1942597.
  • Huang, Hongyao: Research partially supported by NSF grant CCF-1750780.
  • Raichel, Benjamin: Research partially supported by NSF grant CCF-1750780.

Cite AsGet BibTex

Kyle Fox, Hongyao Huang, and Benjamin Raichel. Clustering with Faulty Centers. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ISAAC.2022.10

Abstract

In this paper we introduce and formally study the problem of k-clustering with faulty centers. Specifically, we study the faulty versions of k-center, k-median, and k-means clustering, where centers have some probability of not existing, as opposed to prior work where clients had some probability of not existing. For all three problems we provide fixed parameter tractable algorithms, in the parameters k, d, and ε, that (1+ε)-approximate the minimum expected cost solutions for points in d dimensional Euclidean space. For Faulty k-center we additionally provide a 5-approximation for general metrics. Significantly, all of our algorithms have a small dependence on n. Specifically, our Faulty k-center algorithms have only linear dependence on n, while for our algorithms for Faulty k-median and Faulty k-means the dependence is still only n^(1 + o(1)).

Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
  • Theory of computation → Computational geometry
Keywords
  • clustering
  • approximation
  • probabilistic input
  • uncertain input

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