Abstract Submodular maximization is well studied in the fields of data mining and machine learning. We study the submodular maximization subject to a cardinality constraint k for large scale scenarios applications under two combined settings. One is that all elements arrive in a streaming fashion, and the other is that some elements may be invalid at last. For this problem, which is called streaming robust submodular maximization (SRSM) problem, we explore an approximation algorithm, returning a subset S from the ground set V with a limit size, such that it represents V and is robust to a broken set E well. Our algorithm only makes one pass over data, and achieves a constant-factor 0.1224 approximation guarantee, independent of the cardinality constraint parameter k . Based on the algorithm for SRSM problem, we continue to discuss this problem over sliding windows, in which we are asked to obtain a proper set that only considers the last W elements, and derive an algorithm with a constant ( 0 . 0612 − ϵ ) -approximation guarantee. At last we also propose numerical experiments on some applications to well demonstrate our algorithm for SRSM problem over sliding windows.

中文翻译：

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用于稳健子模块最大化的流算法

摘要 子模块最大化在数据挖掘和机器学习领域得到了很好的研究。我们研究了在两种组合设置下的大规模场景应用的基数约束 k 下的子模块最大化。一个是所有元素以流方式到达，另一个是某些元素可能最终无效。对于这个称为流鲁棒子模最大化 (SRSM) 问题的问题，我们探索了一种近似算法，从具有限制大小的地面集 V 中返回子集 S，这样它表示 V 并且对破碎集 E 具有良好的鲁棒性. 我们的算法只对数据进行一次传递，并实现了常数因子 0.1224 的近似保证，与基数约束参数 k 无关。基于SRSM问题的算法，我们继续在滑动窗口上讨论这个问题，其中我们被要求获得一个只考虑最后 W 个元素的适当集合，并导出一个具有常数 ( 0 . 0612 − ϵ ) -近似保证的算法。最后，我们还提出了一些应用的数值实验，以很好地证明我们在滑动窗口上解决 SRSM 问题的算法。