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Maximization of Constrained Non-submodular Functions

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Computing and Combinatorics (COCOON 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11653))

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Abstract

We investigate a non-submodular maximization problem subject to a p-independence system constraint, where the non-submodularity of the utility function is characterized by a series of parameters, such as submodularity (supmodularity) ratio, generalized curvature, and zero order approximate submodularity coefficient, etc. Inspired by Feldman et al. [15] who consider a non-monotone submodular maximization with a p-independence system constraint, we extend their Repeat-Greedy algorithm to non-submodular setting. While there is no general reduction to convert algorithms for submodular optimization problems to non-submodular optimization problems, we are able to show the extended Repeat-Greedy algorithm has an almost constant approximation ratio for non-monotone non-submodular maximization.

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Acknowledgments

The first two authors are supported by Natural Science Foundation of China (Nos. 11531014, 11871081). The third author is supported by Natural Sciences and Engineering Research Council of Canada (No. 283106). The fourth author is supported by China Postdoctoral Science Foundation funded project (No. 2018M643233) and Natural Science Foundation of China (No. 61433012). The fifth author is supported by Natural Science Foundation of Shanxi province (No. 201801D121022).

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Authors and Affiliations

  1. Department of Operations Research and Scientific Computing, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Ruiqi Yang & Dachuan Xu

  2. Faculty of Business, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

    Donglei Du

  3. Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, People’s Republic of China

    Yicheng Xu

  4. Department of Mathematics, Taiyuan Normal University, Jinzhong, 030619, Shanxi, People’s Republic of China

    Xihong Yan

Authors
  1. Ruiqi Yang
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  2. Dachuan Xu
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  3. Donglei Du
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  4. Yicheng Xu
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  5. Xihong Yan
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Corresponding author

Correspondence to Yicheng Xu .

Editor information

Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. Xidian University, Xi'an, China

    Zhenhua Duan

  3. Xidian University, Xi'an, China

    Cong Tian

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Yang, R., Xu, D., Du, D., Xu, Y., Yan, X. (2019). Maximization of Constrained Non-submodular Functions. In: Du, DZ., Duan, Z., Tian, C. (eds) Computing and Combinatorics. COCOON 2019. Lecture Notes in Computer Science(), vol 11653. Springer, Cham. https://doi.org/10.1007/978-3-030-26176-4_51

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  • DOI: https://doi.org/10.1007/978-3-030-26176-4_51

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26175-7

  • Online ISBN: 978-3-030-26176-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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