Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this classic problem in the fully dynamic setting, where elements can be both inserted and deleted in real-time. Our main result is a randomized algorithm that maintains an efficient data structure with an $\tilde{O}(k^2)$ amortized update time (in the number of additions and deletions) and yields a $4$-approximate solution, where $k$ is the rank of the matroid.

翻译：在拟阵约束下最大化单调子模函数是一个经典算法问题，在数据挖掘和机器学习中有多种应用。我们在全动态设置下研究这一经典问题，其中元素可以实时插入和删除。我们的主要结果是一种随机算法，该算法维护一个高效的数据结构，其摊销更新次数（即增加和删除的次数）为 $\tilde{O}(k^2)$，并产生一个 $4$ 近似解，其中 $k$ 是拟阵的秩。