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Two-stage submodular maximization problem beyond nonnegative and monotone

Published online by Cambridge University Press:  16 November 2021

Zhicheng Liu ,
Hong Chang ,
Ran Ma ,
Donglei Du  and
Xiaoyan Zhang Open the ORCID record for Xiaoyan Zhang [Opens in a new window]
Zhicheng Liu
Affiliation:
College of Taizhou, Nanjing Normal University, Taizhou 225300, P. R. China
Hong Chang
Affiliation:
School of Mathematical Science, Institute of Mathematics, Nanjing Normal University, Nanjing 210023, P. R. China
Ran Ma
Affiliation:
School of Management Engineering, Qingdao University of Technology, Qingdao 266520, P. R. China
Donglei Du
Affiliation:
Faculty of Management, University of New Brunswick, Fredericton, New Brunswick E3B 5A3, Canada
Xiaoyan Zhang*
Affiliation:
School of Mathematical Science, Institute of Mathematics, Nanjing Normal University, Nanjing 210023, P. R. China
*
*Corresponding author. Emails: royxyzhang@gmail.com; zhangxiaoyan@njnu.edu.cn
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Abstract

We consider a two-stage submodular maximization problem subject to a cardinality constraint and k matroid constraints, where the objective function is the expected difference of a nonnegative monotone submodular function and a nonnegative monotone modular function. We give two bi-factor approximation algorithms for this problem. The first is a deterministic $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}}}} \right),1} \right)$-approximation algorithm, and the second is a randomized $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}}}} \right) - \varepsilon ,1} \right)$-approximation algorithm with improved time efficiency.

Keywords

Submodular maximizationgreedy algorithmmatroid

Information

Type
Special Issue: TAMC 2022
Information
Mathematical Structures in Computer Science , Volume 34 , Special Issue 3: Theory and Applications of Models of Computation , March 2024 , pp. 211 - 226
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

†

A preliminary version of the paper Liu et al. (2020) appeared in the 16th Annual Conference on Theory and Applications of Models of Computation 2020.

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