Maximizing Submodular+Supermodular Functions Subject to a Fairness Constraint  

作　　者：Zhenning Zhang Kaiqiao Meng Donglei Du Yang Zhou 

机构地区：[1]Beijing Institute for Scientific and Engineering Computing,Beijing University of Technology,Beijing 100124,China [2]Faculty of Management,University of New Brunswick,Fredericton E3B 5A3,Canada [3]School of Mathematics and Statistics,Shandong Normal University,Jinan 250014,China

出　　处：《Tsinghua Science and Technology》2024年第1期46-55,共10页清华大学学报（自然科学版（英文版）

基　　金：The first author was supported by the National Natural Science Foundation of China(Nos.12001025 and 12131003);The second author was supported by the Spark Fund of Beijing University of Technology(No.XH-2021-06-03);The third author was supported by the Natural Sciences and Engineering Research Council of Canada(No.283106);the Natural Science Foundation of China(Nos.11771386 and 11728104);The fourth author is supported by the National Natural Science Foundation of China(No.12001335).

摘　　要：We investigate the problem of maximizing the sum of submodular and supermodular functions under a fairness constraint.This sum function is non-submodular in general.For an offline model,we introduce two approximation algorithms:A greedy algorithm and a threshold greedy algorithm.For a streaming model,we propose a one-pass streaming algorithm.We also analyze the approximation ratios of these algorithms,which all depend on the total curvature of the supermodular function.The total curvature is computable in polynomial time and widely utilized in the literature.

关 键 词：submodular function supermodular function fairness constraint greedy algorithm threshold greedy algorithm streaming algorithm 

分 类 号：C912.3[经济管理] O157.5[社会学]