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Non-monotone k-Submodular Function Maximization with Individual Size Constraints

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Computational Data and Social Networks (CSoNet 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13831))

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Abstract

In the problem of maximizing non-monotone k-submodular function f under individual size constraints, the goal is to maximize the value of k disjoint subsets with size upper bounds \(B_1,B_2,\ldots ,B_k\), respectively. This problem generalized both submodular maximization and k-submodular maximization problem with total size constraint. In this paper, we propose two results about this kind of problem. One is a \(\frac{1}{B_m+4}\)-approximation algorithm, where \(B_m=\max \{B_1,B_2,\ldots ,B_k\}\). The other is a bi-criteria algorithm with approximation ratio \(\frac{1}{4}\), where each subset is allowed to exceed the size constraint by up to \(B_m\), and in the worst case, only one subset will exceed \(B_m\).

Supported by Natural Science Foundation of Shandong Province of China (Nos. ZR2020MA029, ZR2021MA100) and National Science Foundation of China (No. 12001335).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People’s Republic of China

    Hao Xiao, Qian Liu, Yang Zhou & Min Li

Authors
  1. Hao Xiao
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  2. Qian Liu
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  3. Yang Zhou
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  4. Min Li
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Correspondence to Min Li .

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Editors and Affiliations

  1. Virginia Commonwealth University, Richmond, VA, USA

    Thang N. Dinh

  2. Yeung Kin Man Academic Building, City University Hong Kong, Kowloon Tong, Hong Kong

    Minming Li

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Xiao, H., Liu, Q., Zhou, Y., Li, M. (2023). Non-monotone k-Submodular Function Maximization with Individual Size Constraints. In: Dinh, T.N., Li, M. (eds) Computational Data and Social Networks . CSoNet 2022. Lecture Notes in Computer Science, vol 13831. Springer, Cham. https://doi.org/10.1007/978-3-031-26303-3_24

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  • DOI: https://doi.org/10.1007/978-3-031-26303-3_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-26302-6

  • Online ISBN: 978-3-031-26303-3

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