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 additionalfairness 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 (\frac{1}{2}-\varepsilon) -approximation algorithm that requires O(\frac{1}{\varepsilon} \cdot \log \frac{k}{\varepsilon}) passes over the stream for any constant \varepsilon>0 . In addition, we design a single-pass streaming algorithm that has the same  (\frac{1}{2}-\varepsilon) approximation ratio when unlimited buffer size and post-processing time is permitted\emph{ \emph{ .
We study the problem of extracting a small subset of representative items from a large data stream. In many data mining and machine learning applications such as social network analysis and recommender systems, this problem can be formulated as maximizing a monotone submodular function subject to a cardinality constraint k. In this work , we consider the setting where data items in the stream belong to one of several disjoint groups and investigate the optimization problem with an additionalfairness constraint that limits selection to a given number of items from each group . We then propose efficient algorithms for the fairness-aware variant of the streaming submodular maximization problem. In particular, we first give a (\frac{1}{2}-\varepsilon) -approximation algorithm that requires O(\frac{1}{\varepsilon} \log \frac{k}{\varepsilon}) passes over the stream for any constant \varepsilon>0 . Moreover, we give a single-pass streaming algorithm that has the same approximation ratio of (\frac{1}{2}-\varepsilon) when unlimited buffer sizes and post-processing time are permitted, and discuss how to adapt it to more practical settings where the buffer sizes are bounded. Finally, we demonstrate the efficiency and effectiveness of our proposed algorithms on two real-world applications, namely\emph{maximum coverage on large graphs and\emph{personalized recommendation .
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