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Two-stage submodular maximization under curvature

Author

Listed:
  • Yanzhi Li

    (University of Science and Technology of China)

  • Zhicheng Liu

    (Beijing University of Technology)

  • Chuchu Xu

    (Nanjing Normal University)

  • Ping Li

    (Central Research Institute, 2012 Labs)

  • Xiaoyan Zhang

    (Nanjing Normal University)

  • Hong Chang

    (Nanjing Normal University)

Abstract

The concept of submodularity has wide applications in data science, artificial intelligence, and machine learning, providing a boost to the investigation of new ideas, innovative techniques, and creative algorithms to solve different submodular optimization problems arising from a diversity of applications. However pure submodular problems only represent a small portion of the problems we are facing in real life applications. In this paper, we further discuss the two-stage submodular maximization problem under a $$\ell $$ ℓ -matroid constraint. We design an approximation algorithm with constant approximation ratio with respect to the curvature, which improves the previous bound. In addition, we generalize our algorithm to the two-stage submodular maximization problem under a $$\ell $$ ℓ -exchange system constraint.

Suggested Citation

  • Yanzhi Li & Zhicheng Liu & Chuchu Xu & Ping Li & Xiaoyan Zhang & Hong Chang, 2023. "Two-stage submodular maximization under curvature," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-16, March.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:2:d:10.1007_s10878-023-01001-0
    DOI: 10.1007/s10878-023-01001-0
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    References listed on IDEAS

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    1. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions - 1," LIDAM Reprints CORE 334, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions," LIDAM Reprints CORE 341, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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