Two-stage non-submodular maximization *,**

The sheer size of modern datasets has led to an urgent need for summarization techniques that can identify representative elements of the data set. Fortunately, the vast majority of data summarization tasks satisfy an intuitive diminishing returns condition known as submodularity, which allows us to find nearly-optimal solutions in linear time. However, for many applications in practice, including experimental design and sparse Gaussian processes, the objective is in general not submodular. To solve these optimization problems, an important research method is to describe the characteristics of the non-submodular functions. The non-submodular function is a hot research topic in the study of nonlinear combinatorial optimizations. In this paper, we combine and generalize the curvature and the generic submodularity ratio to design an approximation algorithm for two-stage nonsubmodular maximization under a matroid constraint. & COPY; 2023 Elsevier B.V. All rights reserved.