Streaming Submodular Maximization with Fairness Constraints
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We study the problem of extracting a small subset of representative items from a large data stream. Following the convention in many data mining and machine learning applications such as data summarization, recommender systems, and social network analysis, the problem is formulated as maximizing a monotone submodular function subject to a cardinality constraint – i.e., the size of the selected subset is restricted to be smaller than or equal to an input integer k. In this paper, we consider the problem with additional fairness constraints, which takes into account the group membership of data items and limits the number of items selected from each group to a given number. We propose efficient algorithms for this fairness-aware variant of the streaming submodular maximization problem. In particular, we first provide a (1/2-ε)-approximation algorithm that requires O(1/ε·logk/ε) passes over the stream for any constant ε>0. In addition, we design a single-pass streaming algorithm that has the same (1/2-ε) approximation ratio when unlimited buffer size and post-processing time is permitted.
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