Fair Clustering in the Sliding Window Model

We study streaming algorithms for proportionally fair clustering, a notion originally suggested by [CKLV17], 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 + ε) factor, there exists a (1 + ε)-approximate sliding window algorithm that uses poly(kε -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.