Multipass Streaming Algorithms for Regularized Submodular Maximization

In this work, we study a $k$-Cardinality Constrained Regularized Submodular Maximization ( $k$-CCRSM) problem, in which the objective utility is expressed as the difference between a non-negative submodular and a modular function. No multiplicative approximation algorithm exists for the regularized model, and most works have focused on designing weak approximation algorithms for this problem. In this study, we consider the $k$-CCRSM problem in a streaming fashion, wherein the elements are assumed to be visited individually and cannot be entirely stored in memory. We propose two multipass streaming algorithms with theoretical guarantees for the above problem, wherein submodular terms are monotonic and nonmonotonic.