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Continuous Greedy Algorithm Submodular Maximization Subject to a Mtroid

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Abstract

In this paper, we consider the problem of maximizing a non-submodular set function subject to a matroid constraint with the continuous generic submodularity ratio \(\gamma \). It quantifies how close a monotone function is to being submodular. As our main contribution, we propose a \((1-e^{-\gamma ^2}-O(\varepsilon ))\)-approximation algorithm when the submodularity ratio is sufficiently large. Our work also can be seen as the first extension of the adaptive sequencing technique in non-submodular case.

Keywords

  • Non-submodular optimization
  • Matroid constraint
  • Submodularity ratio
  • Adaptive sequencing

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Acknowledgements

The first and second authors are supported by Beijing Natural Science Foundation Project (No. Z200002) and National Natural Science Foundation of China (No. 11871081). The third author is supported by National Natural Science Foundation of China (No. 11871081). The fourth author is supported by Natural Science Foundation of Shandong Province of China (No. ZR2019PA004) and National Natural Science Foundation of China (No. 12001335).

Author information

Authors and Affiliations

  1. Department of Operations Research and Information Engineering, Beijing University of Technology, Beijing, 100124, People's Republic of China

    Xin Sun & Dachuan Xu

  2. School of Computer Science and Technology, Shandong Jianzhu University, Jinan, 250101, People's Republic of China

    Dongmei Zhang

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

    Yang Zhou

Corresponding author

Correspondence to Yang Zhou .

Editor information

Editors and Affiliations

  1. University of South Florida, Tampa, FL, USA

    Sriram Chellappan

  2. The University of Texas at San Antonio, San Antonio, TX, USA

    Prof. Kim-Kwang Raymond Choo

  3. New Jersey Institute of Technology, Newark, NJ, USA

    NhatHai Phan

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Sun, X., Xu, D., Zhang, D., Zhou, Y. (2020). An Adaptive Algorithm for Maximization of Non-submodular Function with a Matroid Constraint. In: Chellappan, S., Choo, KK.R., Phan, N. (eds) Computational Data and Social Networks. CSoNet 2020. Lecture Notes in Computer Science(), vol 12575. Springer, Cham. https://doi.org/10.1007/978-3-030-66046-8_1

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  • DOI : https://doi.org/10.1007/978-3-030-66046-8_1

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  • Print ISBN: 978-3-030-66045-1

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