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International Conference on Algorithmic Applications in Management

AAIM 2022: Algorithmic Aspects in Information and Management pp 156–167Cite as

Guarantees for Maximization of k-Submodular Functions with a Knapsack and a Matroid Constraint

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

Abstract

A k-submodular function is a generalization of a submodular function, whose definition domain is the collection of k disjoint subsets. In our paper, we apply a greedy and local search technique to obtain a \(\frac{1}{6}(1-e^{-2})\)-approximate algorithm for the problem of maximizing a k-submodular function subject to the intersection of a knapsack constraint and a matroid constraint. Furthermore, we use a special analytical method to improve the approximation ratio to \(\frac{1}{3}(1-e^{-3})\), when the k-submodular function is monotone.

Supported by National Science Foundation of China (No. 12001335) and Natural Science Foundation of Shandong Province of China (Nos. ZR2019PA004, ZR2020MA029, ZR2021MA100).

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Authors and Affiliations

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

    Kemin Yu, Min Li, Yang Zhou & Qian Liu

Authors
  1. Kemin Yu
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  2. Min Li
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  3. Yang Zhou
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  4. Qian Liu
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Corresponding author

Correspondence to Qian Liu .

Editor information

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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Yu, K., Li, M., Zhou, Y., Liu, Q. (2022). Guarantees for Maximization of k-Submodular Functions with a Knapsack and a Matroid Constraint. 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_14

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  • DOI: https://doi.org/10.1007/978-3-031-16081-3_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-16080-6

  • Online ISBN: 978-3-031-16081-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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