  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.
