Fully Dynamic Submodular Maximization over Matroids
This work addresses a classic algorithmic problem with applications in data mining and machine learning, providing a dynamic solution for real-time updates, though it is incremental as it builds on existing static methods.
The paper tackles the problem of maximizing monotone submodular functions under a matroid constraint in a fully dynamic setting with real-time insertions and deletions, achieving a randomized algorithm with $ ilde{O}(k^2)$ amortized update time and a 4-approximate solution.
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.