Dynamic Clustering to Minimize the Sum of Radii

Authors Monika Henzinger, Dariusz Leniowski, Claire Mathieu

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Monika Henzinger
Dariusz Leniowski
Claire Mathieu

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Monika Henzinger, Dariusz Leniowski, and Claire Mathieu. Dynamic Clustering to Minimize the Sum of Radii. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 48:1-48:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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.
  • dynamic algorithm
  • clustering
  • approximation
  • doubling dimension


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