Fully Dynamic Submodular Maximization over Matroids

Paul Duetting, Federico Fusco, Silvio Lattanzi, Ashkan Norouzi-Fard, Morteza Zadimoghaddam

Abstract: 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.

Submission Number: 2847