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Fully Dynamic k-Center Clustering with Outliers

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Abstract

We consider the robust version of the classic k-center clustering problem, where we wish to remove up to z points (outliers), so as to be able to cluster the remaining points in k clusters with minimum maximum radius. We study such a problem under the fully dynamic adversarial model, where points can be inserted or deleted arbitrarily. In this setting, the main goal is to design algorithms that maintain a high quality solution at any point in time, while requiring a “small” amortized cost, i.e. a “small” number of operations per insertion or deletion, on average. In our work, we provide the first constant bi-criteria approximation algorithm for such a problem with its amortized cost being independent of both z and the size of the current input. We also complement our positive result with a lower bound showing that any constant (non bi-criteria) approximation algorithm has amortized cost at least linear in z. Finally, we conduct an in-depth experimental analysis of our algorithm on Twitter, Flickr, and Air-Quality datasets showing the effectiveness of our approach.

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Notes

  1. We note here that the known coresets for k-center with outliers do not imply an algorithm with bounded amortized update time for such a problem, in general metric.

  2. However, for practical implementation, we could possibly re-use the underlying intermediate data structures.

  3. https://github.com/fe6Bc5R4JvLkFkSeExHM/k-center/tree/master/dataset.

  4. http://yfcc100m.appspot.com/.

  5. https://archive.ics.uci.edu/ml/datasets/Beijing+Multi-Site+Air-Quality+Data.

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Acknowledgements

T-H. Hubert Chan was partially supported by the Hong Kong RGC under the grants 17201220, 17202121 and 17203122. The conference version of this paper has appeared in COCOON 2022 [23].

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Authors and Affiliations

  1. University of Hong Kong, Hong Kong, China

    T.-H. Hubert Chan & Bo Wang

  2. Google Research, Zurich, Switzerland

    Silvio Lattanzi

  3. Telecom Paris, Institut Polytechnique de Paris, Paris, France

    Mauro Sozio

Authors
  1. T.-H. Hubert Chan
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  2. Silvio Lattanzi
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  3. Mauro Sozio
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  4. Bo Wang
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Contributions

Sozio had the initial ideas for the project. Sozio and Chan wrote the algorithms and their analysis. Lattanzi wrote the lower bound proof. Wang conducted the experiments. All authors have contributed to the editing and reviewing of the manuscript.

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Correspondence to T.-H. Hubert Chan.

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Chan, TH.H., Lattanzi, S., Sozio, M. et al. Fully Dynamic k-Center Clustering with Outliers. Algorithmica 86, 171–193 (2024). https://doi.org/10.1007/s00453-023-01159-3

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