Maximizing the Ratio of Monotone DR-Submodular Functions on Integer Lattice

被引：0
|
作者：
Chen, Sheng-Min-Jie [1 ]
Du, Dong-Lei [2 ]
Yang, Wen-Guo [1 ]
Gao, Sui-Xiang [1 ]
机构：
[1] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
[2] Univ New Brunswick, Fac Management, Fredericton, NB, Canada
来源：
JOURNAL OF THE OPERATIONS RESEARCH SOCIETY OF CHINA | 2025年 / 13卷 / 01期
基金：
加拿大自然科学与工程研究理事会; 中国国家自然科学基金; 芬兰科学院;
关键词：
DR-submodular maximization; Integer lattice; Threshold decrease algorithm; ALGORITHMS; APPROXIMATIONS;
D O I：
10.1007/s40305-023-00469-1
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
In this work, we focus on maximizing the ratio of two monotone DR-submodular functions on the integer lattice. It is neither submodular nor supermodular. We prove that the Threshold Decrease Algorithm is a 1 - e(-(1-kg)) - e approximation ratio algorithm. Additionally, we construct the relationship between maximizing the ratio of two monotone DR-submodular functions and maximizing the difference of two monotone DR-submodular functions on the integer lattice. Based on this relationship, we combine the dichotomy technique and Threshold Decrease Algorithm to solve maximizing the difference of two monotone DR-submodular functions on the integer lattice and prove its approximation ratio is f (x)-g(x) ? 1-e(-(1-kg)) f (x*)-g(x*)- e. To the best of our knowledge, before us, there was no work to focus on maximizing the ratio of two monotone DR-submodular functions on integer lattice by using the Threshold Decrease Algorithm.
引用
收藏
页码：142 / 160
页数：19
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