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Open Access

Two-Stage Submodular Maximization Under Knapsack Problem

Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing 100124, China
College of Taizhou, Nanjing Normal University, Taizhou 225300, China
Faculty of Management, University of New Brunswick, Fredericton, E3B 5A3, Canada
School of Mathematical Science, Institute of Mathematics, and Ministry of Education Key Laboratory of NSLSCS, Nanjing Normal University, Nanjing 210023, China
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Abstract

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 fj, j=1,2,…,m, and each fj measures the similarity of each article in category j. We present a constant-approximation algorithm for this problem.

Keywords

submodular functionknapsack constraintmatroid

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Tsinghua Science and Technology
Volume 29 Issue 6,
December 2024
Pages 1703-1708
DOI: 10.26599/TST.2023.9010107
Cite this article:
Liu Z, Jin J, Du D, et al. Two-Stage Submodular Maximization Under Knapsack Problem. Tsinghua Science and Technology, 2024, 29(6): 1703-1708. https://doi.org/10.26599/TST.2023.9010107

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Received: 15 December 2022
Revised: 08 March 2023
Accepted: 17 September 2023
Published: 20 June 2024
© The Author(s) 2024.

The articles published in this open access journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
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