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 ?. The goal is to select a subset S subset of Omega of size at most l such that 1/m Sigma(f is an element of F)maxT subset of S,T is an element of If(T) is maximized, where I denotes a specificallydefined 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. (C) 2020 Elsevier B.V. All rights reserved.