Fully Dynamic Submodular Maximization over Matroids

Paul Duetting, Federico Fusco, Silvio Lattanzi, Ashkan Norouzi-Fard, Morteza Zadimoghaddam
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:8821-8835, 2023.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-duetting23a, title = {Fully Dynamic Submodular Maximization over Matroids}, author = {Duetting, Paul and Fusco, Federico and Lattanzi, Silvio and Norouzi-Fard, Ashkan and Zadimoghaddam, Morteza}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {8821--8835}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/duetting23a/duetting23a.pdf}, url = {https://proceedings.mlr.press/v202/duetting23a.html}, 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.} }
Endnote
%0 Conference Paper %T Fully Dynamic Submodular Maximization over Matroids %A Paul Duetting %A Federico Fusco %A Silvio Lattanzi %A Ashkan Norouzi-Fard %A Morteza Zadimoghaddam %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-duetting23a %I PMLR %P 8821--8835 %U https://proceedings.mlr.press/v202/duetting23a.html %V 202 %X 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.
APA
Duetting, P., Fusco, F., Lattanzi, S., Norouzi-Fard, A. & Zadimoghaddam, M.. (2023). Fully Dynamic Submodular Maximization over Matroids. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:8821-8835 Available from https://proceedings.mlr.press/v202/duetting23a.html.

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