The research leading to these results have been supported by the Research Council of Norway via the project BWCA (grant no. 314528), European Research Council (ERC) via grant LOPPRE, reference 819416, and DFG Research Group ADYN via grant DFG 411362735. Open access funding provided by University of Bergen (incl Haukeland University Hospital)
Theory of Computing Systems
Parameterized approximation -- Kernelization
In this work, we study the k-median clustering problem with an additional equal-size constraint on the clusters from the perspective of parameterized preprocessing. Our main result is the first lossy (2-approximate) polynomial kernel for this problem parameterized by the cost of clustering. We complement this result by establishing lower bounds for the problem that eliminate the existence of an (exact) kernel of polynomial size and a PTAS.
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Bandyapadhyay, S., Fomin, F. V., Golovach, P. A., Purohit, N., & Simonov, K. (2023). Lossy kernelization of same-size clustering. Theory of Computing Systems, 1-40.