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A constrained two-stage submodular maximization
Theoretical Computer Science ( IF 0.718 ) Pub Date : 2020-05-21 , DOI: 10.1016/j.tcs.2020.05.024
Ruiqi Yang; Shuyang Gu; Chuangen Gao; Weili Wu; Hua Wang; Dachuan Xu

In this paper, we investigate the two-stage submodular maximization problem, where there is a collection F={f1,...,fm} 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 1m∑f∈FmaxT⊆S,T∈I⁡f(T) is maximized, where I denotes a specific-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.
更新日期:2020-05-21

 

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