Fully Dynamic k-Center Clustering with Outliers

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.