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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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 361; pp. 48 - 68
Main Authors Lai, Xiaoyan, Shi, Yishuo
Format Journal Article
LanguageEnglish
Published Elsevier B.V 30.01.2025
Subjects
Greedy algorithm
Non-monotone
Non-submodular
Non-submodular constraint
Non-submodular constraint
Greedy algorithm
Non-submodular
Non-monotone
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Summary: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.
ISSN:0166-218X
DOI:10.1016/j.dam.2024.09.022