On Maximizing the Difference Between an Approximately Submodular Function and a Linear Function Subject to a Matroid Constraint

被引：2
|
作者：
Wang, Yijing [1 ]
Xu, Yicheng [2 ,3 ]
Yang, Xiaoguang [1 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
[2] Chinese Acad Sci, Shenzhen Inst Adv Technol, Shenzhen 518055, Peoples R China
[3] Guangxi Key Lab Cryptog & Informat Secur, Guilin 541004, Peoples R China
来源：
COMBINATORIAL OPTIMIZATION AND APPLICATIONS, COCOA 2021 | 2021年 / 13135卷
关键词：
Approximately submodular; Matroid constraint; Bicriteria algorithm; Massive data; OPTIMIZATION;
D O I：
10.1007/978-3-030-92681-6_7
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper, we investigate the problem of maximizing the difference between an approximately submodular function and a non-negative linear function subject to a matroid constraint. This model has widespread applications in real life, such as the team formation problem in labor market and the assortment optimization in sales market. We provide a bicriteria approximation algorithm with bifactor ratio (gamma/1+gamma, 1), where gamma is an element of (0, 1] is a parameter to characterize the approximate submodularity. Our result extends Ene's recent work on maximizing the difference between a monotone submodular function and a linear function. Also, a generalized version of the proposed algorithm is capable to deal with huge volume data set.
引用
收藏
页码：75 / 85
页数：11
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