Approximation algorithm of maximizing non-monotone non-submodular functions under knapsack constraint

The maximization of non-negative monotone submodular functions under a certain constraint is intensively studied. However, there are few works considering the maximization of non-monotone non-submodular functions, which even might be negative. These functions also have many applications, such as opt...

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Bibliographic Details
Published inTheoretical computer science Vol. 990; p. 114409
Main Authors Shi, Yishuo, Lai, Xiaoyan
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.04.2024
Subjects
Greedy algorithm
Knapsack constraint
Non-monotone
Non-submodular
Greedy algorithm
Non-submodular
Non-monotone
Knapsack constraint
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Summary:The maximization of non-negative monotone submodular functions under a certain constraint is intensively studied. However, there are few works considering the maximization of non-monotone non-submodular functions, which even might be negative. These functions also have many applications, such as optimal marketing for revenue maximization over social networks, budget allocation problems, and Epidemic transmission, etc. In our paper, we discuss the maximization of the non-monotone non-submodular functions under a knapsack constraint, which even might be negative, and explore the performance under the greedy algorithm. We obtain some improved approximate ratios, for the functions with different properties, such as the non-negative weak-monotone weak-submodular functions, and the weak-submodular weak-supermodular functions that might be negative. Moreover, we generalize the results to the functions with weak subadditivity and curvature.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2024.114409