Keywords: fair clustering, sliding window model
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 exist in the insertion-only model, surprisingly no algorithm can achieve finite ratio without violating the fairness constraint in 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 by a multiplicative $\varepsilon$ 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.
Primary Area: alignment, fairness, safety, privacy, and societal considerations
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Submission Number: 9108
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