Scalable and Improved Algorithms for Individually Fair Clustering

Mohammadhossein Bateni, Vincent Cohen-Addad, Alessandro Epasto, Silvio Lattanzi

Keywords: fairness, clustering, individual fairness, multi-objective

TL;DR: We developed efficient algorithms with improved tradeoffs for individual fairness in clustering

Abstract:

We present scalable and improved algorithms for the individually fair ($p$, $k$)-clustering problem
introduced by Jung et al and Mahabadi et al.
Given $n$ points $P$ in a metric space,
let $\delta(x)$ for $x\in P$ be the radius of the smallest ball around $x$
containing at least $\nicefrac nk$ points.

In this work, we present two main contributions.
We first present local-search algorithms improving prior work along cost and maximum fairness violation.
Then we design a fast local-search algorithm
that runs in $\tO(nk^2)$ time and obtains a bicriteria $(O(1), 6)$ approximation.
Finally we show empirically that not only is our algorithm much faster than prior work, but it also produces lower-cost solutions.