Non-monotone Submodular Optimization: p -Matchoid Constraints and Fully Dynamic Setting

Submodular maximization subject to a $p$-matchoid constraint has various applications in machine learning, particularly in tasks such as feature selection, video and text summarization, movie recommendation, graph-based learning, and constraint-based optimization. We study this problem in the dynamic setting, where a sequence of insertions and deletions of elements to a $p$-matchoid $\mathcal{M}(\mathcal{V},\mathcal{I})$ occurs over time and the goal is to efficiently maintain an approximate solution. We propose a dynamic algorithm for non-monotone submodular maximization under a $p$-matchoid constraint.