Knapsack 问题下的两阶段次模态最大化

IF 6.6 1区计算机科学 Q1 Multidisciplinary

Tsinghua Science and Technology Pub Date : 2024-06-20 DOI:10.26599/TST.2023.9010107

Zhicheng Liu;Jing Jin;Donglei Du;Xiaoyan Zhang

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引用次数: 0

摘要

机器学习和组合优化领域已经广泛研究了万有引力约束下的两阶段子模块最大化问题。本文考虑的是 knapsack 约束。在这个问题中，我们给出了 $n$ 文章和 $m$ 类别，目标是选择一个能使函数 $F(S)$ 最大化的文章子集。函数 $F(S)$ 由 $m$ 单调子模态函数 $f_{j}, j=1,2, \ldots, m$ 组成，每个 $f_{j}$ 衡量类别 $j$ 中每篇文章的相似度。我们为这个问题提出了一种常量逼近算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Two-Stage Submodular Maximization Under Knapsack Problem

Two-stage submodular maximization problem under cardinality constraint has been widely studied in machine learning and combinatorial optimization. In this paper, we consider knapsack constraint. In this problem, we give $n$ articles and $m$ categories, and the goal is to select a subset of articles that can maximize the function $F(S)$ . Function $F(S)$ consists of $m$ monotone submodular functions $f_{j}, j=1,2, \ldots, m$ , and each $f_{j}$ measures the similarity of each article in category $j$ . We present a constant-approximation algorithm for this problem.

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来源期刊

Tsinghua Science and Technology COMPUTER SCIENCE, INFORMATION SYSTEMSCOMPU-COMPUTER SCIENCE, SOFTWARE ENGINEERING

CiteScore

10.20

自引率

10.60%

发文量

2340

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.