A Semi-streaming Algorithm for Monotone Regularized Submodular Maximization with a Matroid Constraint

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  • 1 School of Mathematical Science, Ocean University of China, Qingdao 266100, Shandong, China;
    2 School of mathematics and statistics, Qingdao University, QingDao 266071, Shandong, China

Received date: 2023-06-04

  Revised date: 2023-08-21

  Online published: 2026-03-16

Supported by

This research was supported in part by the National Natural Science Foundation of China (No.12171444).

Abstract

In the face of large-scale datasets in many practical problems, it is an effective method to design approximation algorithms for maximizing a regularized submodular function in a semi-streaming model. In this paper, we study the monotone regularized submodular maximization with a matroid constraint and present a single-pass semistreaming algorithm using multilinear extension function and greedy idea. We show that our algorithm has an approximation ratio of $\left(\frac{(\beta-1)\left(1-\mathrm{e}^{-\alpha}\right)}{\beta+\alpha \beta-\alpha}, \frac{\beta(\beta-1)\left(1-\mathrm{e}^{-\alpha}\right)}{\beta+\alpha \beta-\alpha}\right)$ and a memory of $O(r(M))$, where $r(M)$ is the rank of the matroid and parameters $\alpha, \beta>1$. Specifically, if $\alpha=1.18$ and $\beta=9.784$, our algorithm is ( $0.302,2.955$ )-approximate. If $\alpha=1.257$ and $\beta=3.669$, our algorithm is $(0.2726,1)$-approximate.

Cite this article

Qing-Qin Nong, Yue Wang, Su-Ning Gong . A Semi-streaming Algorithm for Monotone Regularized Submodular Maximization with a Matroid Constraint[J]. Journal of the Operations Research Society of China, 2026 , 14(1) : 162 -178 . DOI: 10.1007/s40305-023-00525-w

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