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arXiv · 2503.05173

Fair Clustering in the Sliding Window Model

Vincent Cohen-Addad·Shaofeng H. -C. Jiang·Qiaoyuan Yang·Yubo Zhang·Samson Zhou
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Abstract

We study streaming algorithms for proportionally fair clustering, a notion originally suggested by Chierichetti et. al. (2017), in the sliding window model. We show that although there exist efficient streaming algorithms in the insertion-only model, surprisingly no algorithm can achieve finite multiplicative ratio without violating the fairness constraint in the sliding window. Hence, the problem of fair clustering is a rare separation between the insertion-only streaming model and the sliding window model. On the other hand, we show that if the fairness constraint is relaxed by a multiplicative $(1+\varepsilon)$ factor, there exists a $(1 + \varepsilon)$-approximate sliding window algorithm that uses $\text{poly}(k\varepsilon^{-1}\log n)$ space. This achieves essentially the best parameters (up to degree in the polynomial) provided the aforementioned lower bound. We also implement a number of empirical evaluations on real datasets to complement our theoretical results.

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Vincent Cohen-Addad, Shaofeng H. -C. Jiang, Qiaoyuan Yang, Yubo Zhang, Samson Zhou. 2025-03-07. Fair Clustering in the Sliding Window Model. https://arxiv.org/abs/2503.05173

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