Streaming Algorithms for Non-Submodular Maximizationon the Integer Lattice  

作　　者：Jingjing Tan Yue Sun Yicheng Xu Juan Zou 

机构地区：[1]School of Mathematics and Information Science,Weifang University,Weifang 261061,China [2]Beijing Institute for Scientific and Engineering Computing,Beijing University of Technology,Beijing 100124,China [3]Shenzhen Institute of Advanced Technology,Chinese Academy of Sciences,Shenzhen 518055,China [4]School of Mathematical Sciences,Qufu Normal University,Qufu 273165,China

出　　处：《Tsinghua Science and Technology》2023年第5期888-895,共8页清华大学学报（自然科学版（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11871081);the Natural Science Foundation of Shandong Province(No.ZR2022MA034);the Guangxi Key Laboratory of Cryptography and Information Security(No.GCIS202116);the Fundamental Research Project of Shenzhen City(No.JCYJ20210324102012033);the National Natural Science Foundation of China(No.11901558);the National Natural Science Foundation of China(No.11801310).

摘　　要：Many practical problems emphasize the importance of not only knowing whether an element is selectedbut also deciding to what extent it is selected,which imposes a challenge on submodule optimization.In this study,we consider the monotone,nondecreasing,and non-submodular maximization on the integer lattice with a cardinalityconstraint.We first design a two-pass streaming algorithm by refining the estimation interval of the optimal value.Foreach element,the algorithm not only decides whether to save the element but also gives the number of reservations.Then,we introduce the binary search as a subroutine to reduce the time complexity.Next,we obtain a one-passstreaming algorithm by dynamically updating the estimation interval of optimal value.Finally,we improve the memorycomplexity of this algorithm.

关 键 词：integer lattice non-submodular streaming algorithm cardinality constraint 

分 类 号：O17[理学—数学]