Fair k-Center Clustering for Data Summarization

Matthäus Kleindessner; Pranjal Awasthi; Jamie Morgenstern

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arXiv · 1901.08628

Fair k-Center Clustering for Data Summarization

Matthäus Kleindessner·Pranjal Awasthi·Jamie Morgenstern

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Abstract

In data summarization we want to choose $k$ prototypes in order to summarize a data set. We study a setting where the data set comprises several demographic groups and we are restricted to choose $k_i$ prototypes belonging to group $i$. A common approach to the problem without the fairness constraint is to optimize a centroid-based clustering objective such as $k$-center. A natural extension then is to incorporate the fairness constraint into the clustering problem. Existing algorithms for doing so run in time super-quadratic in the size of the data set, which is in contrast to the standard $k$-center problem being approximable in linear time. In this paper, we resolve this gap by providing a simple approximation algorithm for the $k$-center problem under the fairness constraint with running time linear in the size of the data set and $k$. If the number of demographic groups is small, the approximation guarantee of our algorithm only incurs a constant-factor overhead.

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BibTeX RIS

Matthäus Kleindessner, Pranjal Awasthi, Jamie Morgenstern. 2019-01-24. Fair k-Center Clustering for Data Summarization. https://arxiv.org/abs/1901.08628

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