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Clustering What Matters in Constrained Settings by Jaiswal, Ragesh; Kumar, Amit is a scholarly article available to read on EtoBox.

What is Clustering What Matters in Constrained Settings about?

Constrained clustering problems generalize classical clustering formulations, e.g., $k$-median, $k$-means, by imposing additional constraints on the feasibility of clustering. There has been significant recent progress in obtaining approximation algorithms for these problems, both in the metric and the Euclidean settings. However, the outlier version of these problems, where the solution is allowed to leave out $m$ points from the clustering, is not well understood. In this work, we give a general framework for reducing the outlier version of a constrained $k$-median or $k$-means problem to the corresponding outlier-free version with only $(1+\varepsilon)$-loss in the approximation ratio. The reduction is obtained by mapping the original instance of the problem to $f(k,m, \varepsilon)$ instances of the outlier-free version, where $f(k, m, \varepsilon) = \left( \frac{k+m}{\varepsilon}\right)^{O(m)}$. As specific applications, we get the following results: - First FPT (in the parameters $k$ and $m$) $(1+\varepsilon)$-approximation algorithm for the outlier version of capacitated $k$-median and $k$-means in Euclidean spaces with hard capacities. - First FPT (in the parameters $k$ and

Author

Jaiswal, Ragesh; Kumar, Amit

Published

2023

Language

EN