A Scalable Algorithm for Individually Fair K-means Clustering
<|reference_start|>A Scalable Algorithm for Individually Fair K-means Clustering: 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.<|reference_end|>
@article{bateni2024a,
    title={A Scalable Algorithm for Individually Fair K-means Clustering},
    author={MohammadHossein Bateni and Vincent Cohen-Addad and Alessandro Epasto
  and Silvio Lattanzi},
    journal={arXiv preprint arXiv:2402.06730},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.06730},
    primaryClass={cs.DS cs.CY cs.LG}
}