我们研究的问题，从一个大的数据流中提取一个小的代表性项目的子集。在许多数据挖掘和机器学习应用中，例如社会网络分析和推荐系统，这个问题可以被公式化为最大化服从基数约束的单调子模函数$k$。在这项工作中，我们考虑设置在流中的数据项属于几个不相交的组之一，并调查的优化问题与一个额外的\emph{fairness}约束，限制选择到一个给定数量的项目从每个组。然后，我们提出了有效的算法的公平性感知的流子模块最大化问题的变体。特别是，我们首先给出了一个$ (\frac{1}{2}-\varepsilon) $近似算法，需要$ O(\frac{1}{\varepsilon} \log \frac{k}{\varepsilon}) $通过流的任何常数$ \varepsilon>0 $。此外，我们给出了一个单通流算法，具有相同的近似比的$(\frac{1}{2}-\varepsilon)$时，无限的缓冲区大小和后处理时间是允许的，并讨论如何适应更实际的设置，缓冲区大小是有界的。最后，我们证明了我们提出的算法的效率和有效性在两个现实世界的应用程序，即\emph{maximum coverage on large graphs}和\emph{personalized recommendation}。
英文摘要：
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 additional \emph{fairness} 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}.
Streaming Algorithms for Diversity Maximization with Fairness Constraints
East China Normal University（华东师范大学）；Universitat Pompeu Fabra（庞培法布拉大学）；Eurecat – Centre Tecnològic de Catalunya（Eurecat——加泰罗尼亚技术中心）；University of Helsinki（赫尔辛基大学）
Improved Streaming Algorithm for Fair $k$-Center Clustering
School of Mathematics and Statistics, Fuzhou University（福州大学数学与统计学院）；School of Integrated Circuits, Guangdong University of Technology（广东工业大学集成电路学院）；School of Accounting, Information Systems and Supply Chain, RMIT University（皇家墨尔本理工大学会计、信息系统和供应链学院）
Constant-Factor Approximations for Doubly Constrained Fair k-Center, k-Median and k-Means
Department of Informatics, University of Cologne, Germany（科隆大学信息学院，德国）；Heinrich Heine University Düsseldorf, Faculty of Mathematics and Natural Sciences, Germany（杜伊斯堡-艾森大学数学与自然科学学院，德国）；Department of Informatics, University of Bonn, Germany（波恩大学信息学院，德国）
