A new greedy strategy for maximizing monotone submodular function under a cardinality constraint - Lu, Cheng; Yang, Wenguo; Gao, Suixiang (Journal of global optimization, 2022)
In this paper, we study the problem of maximizing a monotone non-decreasing submodular function f : 2 Ω → R + subject to a cardinality constraint, i.e., max { f ( A ) : | A | ≤ k , A ⊆ Ω } . We propose a deterministic algorithm based on a new greedy strategy for solving this problem. We prove that when the objective function f satisfies certain assumptions, the algorithm we propose can return a 1 - κ f ( 1 - 1 k ) k approximate solution with O ( kn ) value oracle queries, where κ f is the curvature of the monotone submodular function f . We also show that our algorithm outperforms the traditional greedy algorithm in some cases. Furthermore, we demonstrate how to implement our algorithm in practice.