A constrained two-stage submodular maximization.

In this paper, we investigate the two-stage submodular maximization problem, where there is a collection F = { f 1 ,... , f m } of m submodular functions which are defined on the same element ground set Ω. The goal is to select a subset S ⊆ Ω of size at most ℓ such that 1 m ∑ f ∈ F max T ⊆ S , T ∈ I ⁡ f (T) is maximized, where I denotes a specifically-defined independence system. We consider the two-stage submodular maximization with a P -matroid constraint and present a (1 / (P + 1)) (1 − 1 / e (P + 1)) -approximation algorithm. Furthermore, we extend the algorithm to the two-stage submodular maximization with a more generalized P -exchange system constraint and show the approximation ratio can be maintained with slightly modifications of the algorithm. [ABSTRACT FROM AUTHOR]