Fully Dynamic Submodular Maximization over Matroids
Paul Dütting Federico Fusco Silvio Lattanzi Ashkan Norouzi-Fard Morteza Zadimoghaddam
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.