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

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2024-09-26 DOI:10.1016/j.dam.2024.09.022

引用次数: 0

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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非次模化约束条件下的非次模化函数最大化近似算法

如今，在Knapsack约束或Cardinality约束下最大化非负和非次模态目标函数的研究已经非常深入。然而，很少有人研究非次模化约束下的非次模化目标函数。而这种情况在实际应用中很多，如流行病传播、传感器安置和特征选择问题等。本文研究了非次模化约束下的非次模化目标函数最大化问题。基于非次模化约束，我们讨论了目标函数最大化的一些特定属性，其中包括负属性，然后通过贪婪算法得到了相应的近似比率。更重要的是，当约束条件变得严格时，这些近似比率可以得到改善。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.