The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this classic problem in the fully dynamic setting, where elements can be both inserted and removed. Our main result is a randomized algorithm that maintains an efficient data structure with a poly-logarithmic amortized update time and yields a $(1/2-\epsilon)$-approximate solution. We complement our theoretical analysis with an empirical study of the performance of our algorithm.

翻译：最大化基数约束下单调子模函数的问题是机器学习和数据挖掘应用的核心，包括数据摘要、稀疏回归和覆盖问题。我们在完全动态场景下研究这一经典问题，其中元素可被插入和删除。我们的主要成果是提出一种随机算法，该算法维护一种具有多项式对数均摊更新时间的高效数据结构，并得到$(1/2-\epsilon)$近似解。我们通过算法性能的实证研究补充了理论分析。