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 semi-streaming algorithm using multilinear extension function and greedy idea. We show that our algorithm has an approximation ratio of \((\frac{(\beta -1)(1-\textrm{e}^{-\alpha })}{\beta +\alpha \beta -\alpha }, \frac{\beta (\beta -1)(1-\textrm{e}^{-\alpha })}{\beta +\alpha \beta -\alpha })\) 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 \((0.272\, 6,1)\)-approximate.
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Q.-Q. Nong contributed to validation, supervision, writing- review and editing. Y. Wang contributed to methodology and writing-original draft. S.-N. Gong contributed to methodology and validation-review.
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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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This research was supported in part by the National Natural Science Foundation of China (No. 12171444).
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Nong, QQ., Wang, Y. & Gong, SN. A Semi-streaming Algorithm for Monotone Regularized Submodular Maximization with a Matroid Constraint. J. Oper. Res. Soc. China (2024). https://doi.org/10.1007/s40305-023-00525-w
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DOI: https://doi.org/10.1007/s40305-023-00525-w
Keywords
- Regularized Submodular Maximization
- Possible Negative Objective
- Matroid Constraint
- Semi-Streaming Algorithm