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Monotone k-Submodular Knapsack Maximization: An Analysis of the Greedy+Singleton Algorithm

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Algorithmic Aspects in Information and Management (AAIM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13513))

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Abstract

This paper studies the problem of maximizing a non-negative monotone k-submodular function. A k-submodular function is a generalization of a submodular function, where the input consists of k disjoint subsets, instead of a single subset. For the problem under a knapsack constraint, we consider the algorithm that returns the better solution between the single element of highest value and the result of the fully greedy algorithm, to which we refer as Greedy+Singleton, and prove an approximation ratio \(\frac{1}{4}(1-\frac{1}{e})\approx 0.158\). Though this ratio is strictly smaller than the best known factor for this problem, Greedy+Singleton is simple, fast, and of special interests. Our experiments demonstrates that the algorithm performs well in terms of the solution quality.

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Acknowledgements

This work is partially supported by Artificial Intelligence and Data Science Research Hub, BNU-HKBU United International College (UIC), No. 2020KSYS007, and by a grant from UIC (No. UICR0400025-21). Zhongzheng Tang is supported by National Natural Science Foundation of China under Grant No. 12101069 and Innovation Foundation of BUPT for Youth (No. 500422309). Chenhao Wang is supported by a grant from UIC (No. UICR0700036-22).

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Authors and Affiliations

  1. BNU-HKBU United International College, Zhuhai, China

    Jingwen Chen & Chenhao Wang

  2. Beijing University of Posts and Telecommunications, Beijing, China

    Zhongzheng Tang

  3. Beijing Normal University, Zhuhai, China

    Chenhao Wang

Authors
  1. Jingwen Chen
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  2. Zhongzheng Tang
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  3. Chenhao Wang
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Correspondence to Chenhao Wang .

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Editors and Affiliations

  1. Guangdong University of Technology, Guangzhou, China

    Qiufen Ni

  2. University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

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Chen, J., Tang, Z., Wang, C. (2022). Monotone k-Submodular Knapsack Maximization: An Analysis of the Greedy+Singleton Algorithm. In: Ni, Q., Wu, W. (eds) Algorithmic Aspects in Information and Management. AAIM 2022. Lecture Notes in Computer Science, vol 13513. Springer, Cham. https://doi.org/10.1007/978-3-031-16081-3_13

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  • DOI: https://doi.org/10.1007/978-3-031-16081-3_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-16080-6

  • Online ISBN: 978-3-031-16081-3

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