A fully dynamic algorithm maintains a (2+ε)-approximate k-center clustering in doubling metrics with polylogarithmic update time independent of k.
Hubert Chan, Arnaud Guerqin, and Mauro Sozio
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Fully Dynamic k-Center Clustering in Doubling Metrics
A fully dynamic algorithm maintains a (2+ε)-approximate k-center clustering in doubling metrics with polylogarithmic update time independent of k.