@article{Liu2024, 
author = {Zhicheng Liu and Jing Jin and Donglei Du and Xiaoyan Zhang},
title = {Two-Stage Submodular Maximization Under Knapsack Problem},
year = {2024},
journal = {Tsinghua Science and Technology},
volume = {29},
number = {6},
pages = {1703-1708},
keywords = {submodular function, knapsack constraint, matroid},
url = {https://www.sciopen.com/article/10.26599/TST.2023.9010107},
doi = {10.26599/TST.2023.9010107},
abstract = {Two-stage submodular maximization problem under cardinality constraint has been widely studied in machine learning and combinatorial optimization. In this paper, we consider knapsack constraint. In this problem, we give  n articles and  m categories, and the goal is to select a subset of articles that can maximize the function  F(S). Function  F(S) consists of  m monotone submodular functions  fj,  j=1,2,…,m, and each  fj measures the similarity of each article in category  j. We present a constant-approximation algorithm for this problem.}
}