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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| Published in | Theoretical computer science Vol. 990; p. 114409 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.04.2024
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| Online Access | Get full text |
| ISSN | 0304-3975 1879-2294 |
| DOI | 10.1016/j.tcs.2024.114409 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 114409 |
| Author | Shi, Yishuo Lai, Xiaoyan |
| Author_xml | – sequence: 1 givenname: Yishuo orcidid: 0000-0002-5604-688X surname: Shi fullname: Shi, Yishuo email: yishuo@wzu.edu.cn – sequence: 2 givenname: Xiaoyan surname: Lai fullname: Lai, Xiaoyan email: 1972906484@qq.com |
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| Cites_doi | 10.1145/502090.502098 10.1007/s10878-021-00719-z 10.1007/BF01588971 10.1016/j.tcs.2020.12.002 10.1287/ijoc.2015.0660 10.1016/j.stamet.2006.11.004 10.1016/S0167-6377(03)00062-2 10.1016/j.orl.2011.10.002 10.1109/MCS.2017.2743518 10.1287/moor.2016.0842 10.1007/s10878-019-00449-3 10.1002/jmv.27506 10.1016/S0020-0190(99)00031-9 10.1016/j.jcss.2021.08.003 10.1007/s10107-018-1324-y 10.1137/090779346 10.1007/s10878-020-00558-4 |
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| Snippet | The maximization of non-negative monotone submodular functions under a certain constraint is intensively studied. However, there are few works considering the... |
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| SubjectTerms | Greedy algorithm Knapsack constraint Non-monotone Non-submodular |
| Title | Approximation algorithm of maximizing non-monotone non-submodular functions under knapsack constraint |
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