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Open Access

Approximating (mB,mP⁢)-Monotone BP Maximization and Extensions

Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing 100124, China
School of Mathematical Sciences, University of Chinese Academy Sciences, Beijing 100049, China
School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
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Abstract

The paper proposes the optimization problem of maximizing the sum of suBmodular and suPermodular (BP) functions with partial monotonicity under a streaming fashion. In this model, elements are randomly released from the stream and the utility is encoded by the sum of partial monotone suBmodular and suPermodular functions. The goal is to determine whether a subset from the stream of size bounded by parameter k subject to the summarized utility is as large as possible. In this work, a threshold-based streaming algorithm is presented for the BP maximization that attains a ((1-κ)/(2-κ)-𝒪⁢(ε))-approximation with 𝒪⁢(1/ε4⁢log3⁡(1/ε)⁢log⁡((2-κ)⁢k/(1-κ)2)) memory complexity, where κ denotes the parameter of supermodularity ratio. We further consider a more general model with fair constraints and present a greedy-based algorithm that obtains the same approximation. We finally investigate this fair model under the streaming fashion and provide a ((1-κ)4/(2-2⁢κ+κ2)2-𝒪⁢(ε))-approximation algorithm.

Keywords

submodular maximizationstreaming modelthreshold techniqueapproximation algorithm

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Tsinghua Science and Technology
Volume 28 Issue 5,
October 2023
Pages 906-915
DOI: 10.26599/TST.2022.9010033
Cite this article:
Yang R, Gao S, Han L, et al. Approximating (mB,mP⁢)-Monotone BP Maximization and Extensions. Tsinghua Science and Technology, 2023, 28(5): 906-915. https://doi.org/10.26599/TST.2022.9010033

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Received: 29 April 2022
Revised: 17 July 2022
Accepted: 22 August 2022
Published: 19 May 2023
© The author(s) 2023.

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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