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A Scalable Algorithm for Individually Fair k-Means Clustering

MohammadHossein Bateni · Vincent Cohen-Addad · Alessandro Epasto · Silvio Lattanzi

MR1 & MR2 - Number 24
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Fri 3 May 8 a.m. PDT — 8:30 a.m. PDT

Abstract: We present a scalable algorithm 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 $n / k$ points. A clustering is then called individually fair if it has centers within distance $\delta(x)$ of $x$ for each $x\in P$. While good approximation algorithms are known for this problem no efficient practical algorithms with good theoretical guarantees have been presented. We design the first fast local-search algorithm that runs in ~$O(nk^2)$ time and obtains a bicriteria $(O(1), 6)$ approximation. Then we show empirically that not only is our algorithm much faster than prior work, but it also produces lower-cost solutions.

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