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 ...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.展开更多
集值折扣{0-1}背包问题(Discounted{0-1}Knapsack Problem with Setup,D{0-1}KPS)指在同一类别中可选择多个项,每个类别对目标函数和约束条件都增加了额外的固定设置成本。提出一种求解D{0-1}KPS的改进动态规划算法,算法针对D{0-1}KPS...集值折扣{0-1}背包问题(Discounted{0-1}Knapsack Problem with Setup,D{0-1}KPS)指在同一类别中可选择多个项,每个类别对目标函数和约束条件都增加了额外的固定设置成本。提出一种求解D{0-1}KPS的改进动态规划算法,算法针对D{0-1}KPS问题本身结构特征,融合多目标优化问题中非支配解集思想,通过利用状态之间的支配与非支配关系,对每个阶段的状态集进行剪枝,形成非支配状态集,从而提出改进动态规划算法。通过实例验证了该算法的有效性和可行性。展开更多
基金supported by the National Natural Science Foundation of China(Nos.12271259 and 12371352)the Zhejiang Provincial Natural Science Foundation of China(No.LY23A010011)+1 种基金the Yongjiang Talent Introduction Programme of Ningbo(No.2021B-011-G)the Natural Sciences and Engineering Research Council of Canada(NSERC)(No.06446).
文摘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.
文摘集值折扣{0-1}背包问题(Discounted{0-1}Knapsack Problem with Setup,D{0-1}KPS)指在同一类别中可选择多个项,每个类别对目标函数和约束条件都增加了额外的固定设置成本。提出一种求解D{0-1}KPS的改进动态规划算法,算法针对D{0-1}KPS问题本身结构特征,融合多目标优化问题中非支配解集思想,通过利用状态之间的支配与非支配关系,对每个阶段的状态集进行剪枝,形成非支配状态集,从而提出改进动态规划算法。通过实例验证了该算法的有效性和可行性。
