Approximation algorithm of maximizing non-submodular functions under non-submodular constraint
Nowadays, maximizing the non-negative and non-submodular objective functions under Knapsack constraint or Cardinality constraint is deeply researched. Nevertheless, few studies study the objective functions with non-submodularity under the non-submodular constraint. And there are many practical appl...
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| Published in | Discrete Applied Mathematics Vol. 361; pp. 48 - 68 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
30.01.2025
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| Online Access | Get full text |
| ISSN | 0166-218X |
| DOI | 10.1016/j.dam.2024.09.022 |
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| Abstract | Nowadays, maximizing the non-negative and non-submodular objective functions under Knapsack constraint or Cardinality constraint is deeply researched. Nevertheless, few studies study the objective functions with non-submodularity under the non-submodular constraint. And there are many practical applications of the situations, such as Epidemic transmission, and Sensor Placement and Feature Selection problem. In this paper, we study the maximization of the non-submodular objective functions under the non-submodular constraint. Based on the non-submodular constraint, we discuss the maximization of the objective functions with some specific properties, which includes the property of negative, and then, we obtain the corresponding approximate ratios by the greedy algorithm. What is more, these approximate ratios could be improved when the constraint becomes tight. |
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| AbstractList | Nowadays, maximizing the non-negative and non-submodular objective functions under Knapsack constraint or Cardinality constraint is deeply researched. Nevertheless, few studies study the objective functions with non-submodularity under the non-submodular constraint. And there are many practical applications of the situations, such as Epidemic transmission, and Sensor Placement and Feature Selection problem. In this paper, we study the maximization of the non-submodular objective functions under the non-submodular constraint. Based on the non-submodular constraint, we discuss the maximization of the objective functions with some specific properties, which includes the property of negative, and then, we obtain the corresponding approximate ratios by the greedy algorithm. What is more, these approximate ratios could be improved when the constraint becomes tight. |
| Author | Shi, Yishuo Lai, Xiaoyan |
| Author_xml | – sequence: 1 givenname: Xiaoyan surname: Lai fullname: Lai, Xiaoyan email: 1972906484@qq.com – sequence: 2 givenname: Yishuo orcidid: 0000-0002-5604-688X surname: Shi fullname: Shi, Yishuo email: yishuo@wzu.edu.cn |
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| Cites_doi | 10.1287/ijoc.2015.0660 10.1287/moor.2016.0842 10.1007/s10878-020-00558-4 10.1007/s10957-022-02145-5 10.1145/502090.502098 10.1016/j.stamet.2006.11.004 10.1145/1367497.1367524 10.1609/aaai.v32i1.11520 10.1002/jmv.27506 10.21437/Interspeech.2011-312 10.1016/j.tcs.2024.114409 10.1007/s10878-022-00978-4 10.1016/j.tcs.2020.12.002 10.1145/956750.956769 10.1017/CBO9781139177801.004 10.1007/s10107-018-1324-y 10.1016/S0167-6377(03)00062-2 10.1016/S0020-0190(99)00031-9 |
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| Keywords | Non-submodular constraint Greedy algorithm Non-submodular Non-monotone |
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