Bicriteria Algorithms for Approximately Submodular Cover Under Streaming Model  

作　　者：Yijing Wang Xiaoguang Yang Hongyang Zhang Yapu Zhang 

机构地区：[1]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China [3]Beijing Institute for Scientific and Engineering Computing,Beijing University of Technology,Beijing 100124,China

出　　处：《Tsinghua Science and Technology》2023年第6期1030-1040,共11页清华大学学报（自然科学版（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Nos.72192804,72192800,and 12201619);the China Postdoctoral Science Foundation(No.2022M723333).

摘　　要：In this paper,we mainly investigate the optimization model that minimizes the cost function such that the cover function exceeds a required threshold in the set cover problem,where the cost function is additive linear,and the cover function is non-monotone approximately submodular.We study the problem under streaming model and propose three bicriteria approximation algorithms.Firstly,we provide an intuitive streaming algorithm under the assumption of known optimal objective value.The intuitive streaming algorithm returns a solution such that its cover function value is no less thanα(1−ϵ)times threshold,and the cost function is no more than(2+ϵ)^(2)/(ϵ^(2)ω^(2))⋅κ,whereκis a value that we suppose for the optimal solution andαis the approximation ratio of an algorithm for unconstrained maximization problem that we can call directly.Next we present a bicriteria streaming algorithm scanning the ground set multi-pass to weak the assumption that we guess the optimal objective value in advance,and maintain the same bicriteria approximation ratio.Finally we modify the multi-pass streaming algorithm to a single-pass one without compromising the performance ratio.Additionally,we also propose some numerical experiments to test our algorithm’s performance comparing with some existing methods.

关 键 词：approximately submodular linear additive streaming model bicriteria algorithm 

分 类 号：O22[理学—运筹学与控制论]