发表机构
Fuzhou University（福州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对背包约束下的非单调子模最大化，提出确定性线性查询算法，达到$(1/4-\varepsilon)$近似比，并通过双准则方法改进查询复杂度。
AI 中文摘要
背包约束下的子模最大化（SMK）是一个基本的组合优化问题，在机器学习和数据挖掘中具有广泛的应用。受查询效率至关重要的大规模应用的推动，我们研究非单调SMK，并专注于具有线性查询复杂度的确定性算法。先前的确定性线性查询算法最多达到$1/5-\varepsilon$的近似比，低于随机算法可达到的$1/4-\varepsilon$比率。我们通过提出一个具有$O(n\log^2(1/\varepsilon)/\varepsilon^2)$次查询的确定性$(1/4-\varepsilon)$近似算法来弥合这一差距。我们的方法根据最大最优元素$r$的成本划分分析：当$r$的成本适中时，我们通过剩余预算枚举改进阈值孪生贪心框架以收紧分析；当$r$的成本较大时，我们将问题简化为双准则子模最大化。作为次要贡献，我们获得了一个具有$O(n\log(1/\varepsilon)/\varepsilon^2)$次查询的$(1/2-\varepsilon, O(1/\varepsilon))$双准则近似，改进了先前的$O(n^2/\varepsilon)$查询界限。
英文摘要
Submodular maximization under a knapsack constraint (SMK) is a fundamental combinatorial optimization problem with broad applications across machine learning and data mining. Motivated by large-scale applications where query efficiency is paramount, we study non-monotone SMK and focus on deterministic algorithms with linear query complexity. Prior deterministic linear-query algorithms achieve at best a $1/5-\varepsilon$ approximation, falling short of the $1/4-\varepsilon$ ratio attainable by randomized algorithms. We close this gap by presenting a deterministic $(1/4-\varepsilon)$-approximation with $O(n\log^2(1/\varepsilon)/\varepsilon^2)$ queries. Our approach partitions the analysis based on the cost of the largest optimal element $r$: when the cost of $r$ is moderate, we refine the threshold-twin-greedy framework via residual-budget enumeration to tighten the analysis; when the cost of $r$ is large, we reduce the problem to bicriteria submodular maximization. As a secondary contribution, we obtain a $(1/2-\varepsilon, O(1/\varepsilon))$-bicriteria approximation with $O(n\log(1/\varepsilon)/\varepsilon^2)$ queries, improving over the previous $O(n^2/\varepsilon)$ query bound.
CommentsISAAC 2026
