{"title":"Maximization of k-Submodular Function with d-Knapsack Constraints Over Sliding Window","authors":"Wenqi Wang;Yuefang Sun;Zhiren Sun;Donglei Du;Xiaoyan Zhang","doi":"10.26599/TST.2023.9010121","DOIUrl":null,"url":null,"abstract":"Submodular function maximization problem has been extensively studied recently. A natural variant of submodular function is k-submodular function, which has many applications in real life, such as influence maximization and sensor placement problem. The domain of a \n<tex>$k$</tex>\n -submodular function has \n<tex>$k$</tex>\n disjoint subsets, and hence includes submodular function as a special case when \n<tex>$k=1$</tex>\n. This work investigates the k-submodular function maximization problem with d-knapsack constraints over the sliding window. Based on the smooth histogram technique, we design a deterministic approximation algorithm. Furthermore, we propose a randomized algorithm to improve the approximation ratio.","PeriodicalId":48690,"journal":{"name":"Tsinghua Science and Technology","volume":"30 2","pages":"488-498"},"PeriodicalIF":6.6000,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10786950","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tsinghua Science and Technology","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10786950/","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Multidisciplinary","Score":null,"Total":0}
引用次数: 0
Abstract
Submodular function maximization problem has been extensively studied recently. A natural variant of submodular function is k-submodular function, which has many applications in real life, such as influence maximization and sensor placement problem. The domain of a
$k$
-submodular function has
$k$
disjoint subsets, and hence includes submodular function as a special case when
$k=1$
. This work investigates the k-submodular function maximization problem with d-knapsack constraints over the sliding window. Based on the smooth histogram technique, we design a deterministic approximation algorithm. Furthermore, we propose a randomized algorithm to improve the approximation ratio.
期刊介绍:
Tsinghua Science and Technology (Tsinghua Sci Technol) started publication in 1996. It is an international academic journal sponsored by Tsinghua University and is published bimonthly. This journal aims at presenting the up-to-date scientific achievements in computer science, electronic engineering, and other IT fields. Contributions all over the world are welcome.