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.
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).
