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Dynamic Clustering to Minimize the Sum of Radii

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Abstract

In this paper, we study the problem of opening centers to cluster a set of clients in a metric space so as to minimize the sum of the costs of the centers and of the cluster radii, in a dynamic environment where clients arrive and depart, and the solution must be updated efficiently while remaining competitive with respect to the current optimal solution. We call this dynamic sum-of-radii clustering problem. We present a data structure that maintains a solution whose cost is within a constant factor of the cost of an optimal solution in metric spaces with bounded doubling dimension and whose worst-case update time is logarithmic in the parameters of the problem.

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Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement No. 340506.

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Authors and Affiliations

  1. Faculty of Computer Science, University of Vienna, Vienna, Austria

    Monika Henzinger & Dariusz Leniowski

  2. IRIF, CNRS, Université de Paris, Paris, France

    Claire Mathieu

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  1. Monika Henzinger
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  2. Dariusz Leniowski
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  3. Claire Mathieu
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Correspondence to Monika Henzinger.

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Henzinger, M., Leniowski, D. & Mathieu, C. Dynamic Clustering to Minimize the Sum of Radii. Algorithmica 82, 3183–3194 (2020). https://doi.org/10.1007/s00453-020-00721-7

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