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.
T-H. Hubert Chan was partially supported by the Hong Kong RGC under the grants 17201220 and 17202121. The work of Mauro Sozio has been carried out in the frame of a cooperation between Huawei Technologies France SASU and Telecom Paris (Grant no. YBN2018125164).
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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.
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Chan, TH.H., Lattanzi, S., Sozio, M., Wang, B. (2022). Fully Dynamic k-Center Clustering with Outliers. In: Zhang, Y., Miao, D., Möhring, R. (eds) Computing and Combinatorics. COCOON 2022. Lecture Notes in Computer Science, vol 13595. Springer, Cham. https://doi.org/10.1007/978-3-031-22105-7_14
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