Approximation Algorithms for Maximization of <i>k</i>-Submodular Function Under a Matroid Constraint

Yuezhu Liu; Yunjing Sun; Min Li

doi:10.26599/TST.2023.9010122

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

Yuezhu Liu, Yunjing Sun, Min Li()

School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China

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Abstract

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 $1 - ε$ , where $ε$ is the probability of algorithm failure. Moreover, we design a streaming algorithm for both monotone and non-monotone objective $k$ -submodular functions.

Keywords

k-submodular matroid constraint deterministic algorithm randomized algorithm streaming algorithm

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Tsinghua Science and Technology

Volume 29 Issue 6,
December 2024

Pages 1633-1641

DOI: 10.26599/TST.2023.9010122

Cite this article:

Liu Y, Sun Y, Li M. Approximation Algorithms for Maximization of k-Submodular Function Under a Matroid Constraint. Tsinghua Science and Technology, 2024, 29(6): 1633-1641. https://doi.org/10.26599/TST.2023.9010122