Two-stage submodular maximization problem beyond nonnegative and monotone - Liu, Zhicheng; Chang, Hong; Ma, Ran; Du, Donglei; Zhang, Xiaoyan (Mathematical structures in computer science, 2024)
We consider a two-stage submodular maximization problem subject to a cardinality constraint and k matroid constraints, where the objective function is the expected difference of a nonnegative monotone submodular function and a nonnegative monotone modular function. We give two bi-factor approximation algorithms for this problem. The first is a deterministic $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}} \right),1} \right)$ -approximation algorithm, and the second is a randomized $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}} \right) - ε ,1} \right)$ -approximation algorithm with improved time efficiency.