Fair k-Centers via Maximum Matching

The field of algorithms has seen a push for fairness, or the removal of inherent bias, in recent history. In data summarization, where a much smaller subset of a data set is chosen to represent the whole of the data, fairness can be introduced by guaranteeing each "demographic group" a specific portion of the representative subset. Specifically, this paper examines this fair variant of the k-centers problem, where a subset of the data with cardinality k is chosen to minimize distance to the rest of the data. Previous papers working on this problem presented both a 3-approximation algorithm with a super-linear runtime and a linear-time algorithm whose approximation factor is exponential in the number of demographic groups. This paper combines the best parts of each algorithm , by presenting a linear-time algorithm with a guaranteed 3-approximation factor, and provides empirical evidence of both the algorithm's runtime and effectiveness.