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Two-Stage Non-submodular Maximization

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Theory and Applications of Models of Computation (TAMC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13571))

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Abstract

The concept of submodularity finds 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. To solve these optimization problems, an important research method is to describe the characteristics of the non-submodular functions. The non-submodular functions is a hot research topic in the study of nonlinear combinatorial optimizations. In this paper, we combine and generalize the curvature and the generic submodularity ratio to design an approximation algorithm for two-stage non-submodular maximization under a matroid constraint.

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References

  1. Balkanski, E., Krause, A., Mirzasoleiman, B., Singer, Y.: Learning sparse combinatorial representations via two-stage submodular maximization. In: ICML, pp. 2207–2216 (2016)

    Google Scholar 

  2. Bian, A.A., Buhmann, J.M., Krause, A., Tschiatschek, S.: guarantees for greedy maximization of non-submodular functions with applications. In: Proceedings of ICML, pp. 498–507 (2017)

    Google Scholar 

  3. Conforti, M., Cornuejols, G.: Submodular set functions, matroids and the greedy algorithm: tight worst-case bounds and some generalizations of the Rado-Edmonds theorem. Discrete Appl. Math. 7(3), 251–274 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gong, S., Nong, Q., Sun, T., Fang, Q., Du, X., Shao, X.: Maximize a monotone function with a generic submodularity ratio. Theor. Comput. Sci. 853, 16–24 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  5. Krause, A., Guestrin, A.: Near-optimal nonmyopic value of information in graphical models. In: UAI, p. 5 (2005)

    Google Scholar 

  6. Laitila, J., Moilanen, A.: New performance guarantees for the greedy maximization of submodular set functions. Optim. Lett. 11, 655–665 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lee, J., Mirrokni, V.S., Nagarajan, V., Sviridenko, M.: Maximizing nonmonotone submodular functions under matroid or knapsack constraints. SIAM J. Discrete Math. 23(4), 2053–2078 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lawrence, N., Seeger, M., Herbrich, R.: Fast sparse gaussian process methods: the informative vector machine. Adv. Neural. Inf. Process. Syst. 1(5), 625–632 (2003)

    Google Scholar 

  9. Mitrovic, M., Kazemi, E., Zadimoghaddam, M., Karbasi, A.: Data summarization at scale: a two-stage submodular approach. In: ICML, pp. 3593–3602 (2018)

    Google Scholar 

  10. Nemhauser, G.L., Wolsey, L.A., Fisher, M.L.: An analysis of approximations for maximizing submodular set functions-i. Math. Program. 14(1), 265–294 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  11. Schulz, A.S., Uhan, N.A.: Approximating the least core value and least core of cooperative games with supermodular costs. Discrete Optim. 10(2), 163–180 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. Stan, S., Zadimoghaddam, M., Krause, A., Karbasi, A.: Probabilistic submodular maximization in sub-linear time. In: ICML, pp. 3241–3250 (2017)

    Google Scholar 

  13. Yang, R., Gu, S., Gao, C., Wu, W., Wang, H., Xu, D.: A constrained two-stage submodular maximization. Theor. Comput. Sci. 853, 57–64 (2021)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The research is supported by NSFC (Nos.12101314,12131003, 11871280,12271259,11971349), Qinglan Project, Natural Science Foundation of Jiangsu Province (No. BK20200723), and Jiangsu Province Higher Education Foundation (No.20KJB110022).

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Authors and Affiliations

  1. School of Mathematical Science and Institute of Mathematics, Nanjing Normal University, Nanjing, 210023, China

    Hong Chang & Xiaoyan Zhang

  2. Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing, 100124, China

    Zhicheng Liu

  3. Shandong Qiguang Information Technology Co. Ltd., Jiading Qu, 253000, China

    Ping Li

Authors
  1. Hong Chang
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  2. Zhicheng Liu
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  3. Ping Li
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  4. Xiaoyan Zhang
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Corresponding author

Correspondence to Xiaoyan Zhang .

Editor information

Editors and Affiliations

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

    Ding-Zhu Du

  2. University of New Brunswick, Fredericton, NB, Canada

    Donglei Du

  3. Tianjin University of Technology, Tianjin, China

    Chenchen Wu

  4. Beijing University of Technology, Beijing, China

    Dachuan Xu

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Chang, H., Liu, Z., Li, P., Zhang, X. (2022). Two-Stage Non-submodular Maximization. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Theory and Applications of Models of Computation. TAMC 2022. Lecture Notes in Computer Science, vol 13571. Springer, Cham. https://doi.org/10.1007/978-3-031-20350-3_22

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  • DOI: https://doi.org/10.1007/978-3-031-20350-3_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-20349-7

  • Online ISBN: 978-3-031-20350-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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