矩阵约束条件下 $k$ 次模态函数最大化的近似算法

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.2023.9010122

Yuezhu Liu;Yunjing Sun;Min Li

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引用次数: 0

摘要

在本文中，我们针对在矩阵约束下最大化非单调 $k$ 次模态函数的问题设计了一种确定性 1/3 近似算法。为了降低该算法的复杂度，我们还提出了一种概率为 $1-\varepsilon$ 的随机 1/3 近似算法，其中 $\varepsilon$ 是算法失败的概率。此外，我们还为单调和非单调目标 $k$ 次模态函数设计了一种流算法。

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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Approximation Algorithms for Maximization of $k$-Submodular Function Under a Matroid Constraint

In this paper, we design a deterministic 1/3-approximation algorithm for the problem of maximizing non-monotone $k$ -submodular function under a matroid constraint. In order to reduce the complexity of this algorithm, we also present a randomized 1/3-approximation algorithm with the probability of $1-\varepsilon$ , where $\varepsilon$ is the probability of algorithm failure. Moreover, we design a streaming algorithm for both monotone and non-monotone objective $k$ -submodular functions.

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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.