Neural Information Processing Systems http://nips.cc/

For this reason, it is important to design algorithms that are able to maintain a stable and high quality solution and that at the same time can process updates efficiently.

Clustering is a fundamental problem in unsupervised learning with several practical applications. In clustering, one is interested in partitioning elements into different groups (i.e.

We present a $O(1)$-approximate fully dynamic algorithm for the $k$-median and $k$-means problems on metric spaces with amortized update time $\tilde O(k)$ and worst-case query time $\tilde O(k^2)$. We complement our theoretical analysis with the first in-depth experimental study for the dynamic $k$-median problem on general metrics, focusing on comparing our dynamic algorithm to the current state-of-the-art by Henzinger and Kale [ESA'20]. Finally, we also provide a lower bound for dynamic $k$-median which shows that any $O(1)$-approximate algorithm with $\tilde O(\text{poly}(k))$ query time must have $\tilde \Omega(k)$ amortized update time, even in the incremental setting.

Maximizing submodular functions has been increasingly used in many applications of machine learning, such as data summarization, recommendation systems, and feature selection. Moreover, there has been a growing interest in both submodular maximization and dynamic algorithms. In 2020, Monemizadeh and Lattanzi, Mitrovic, Norouzi-Fard, Tarnawski, and Zadimoghaddam initiated developing dynamic algorithms for the monotone submodular maximization problem under the cardinality constraint $k$. In 2022, Chen and Peng studied the complexity of this problem and raised an important open question: \emph{Can we extend [fully dynamic] results (algorithm or hardness) to non-monotone submodular maximization?}. We affirmatively answer their question by demonstrating a reduction from maximizing a non-monotone submodular function under the cardinality constraint $k$ to maximizing a monotone submodular function under the same constraint. Through this reduction, we obtain the first dynamic algorithms to solve the non-monotone submodular maximization problem under the cardinality constraint $k$. Our algorithms maintain an $(8+\epsilon)$-approximate of the solution and use expected amortized $O(\epsilon^{-3}k^3\log^3(n)\log(k))$ or $O(\epsilon^{-1}k^2\log^3(k))$ oracle queries per update, respectively.