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Beyond Pointwise Submodularity: Non-monotone Adaptive Submodular Maximization Subject to Knapsack and k-System Constraints

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Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO 2021)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 363))

Abstract

Although the knapsack-constrained and k-system-constrained non-monotone adaptive submodular maximization have been well studied in the literature, it has only been settled given the additional assumption of pointwise submodularity. In this paper, we remove the common assumption on pointwise submodularity and propose the first approximation solutions for both knapsack and k-system constrained adaptive submodular maximization problems. Inspired by two recent studies on non-monotone adaptive submodular maximization, we develop a sampling-based randomized algorithm that achieves a \(\frac{1}{10}\) approximation for the case of a knapsack constraint and that achieves a \(\frac{1}{2k+4}\) approximation ratio for the case of a k-system constraint.

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Authors and Affiliations

  1. Naveen Jindal School of Management, University of Texas at Dallas, Richardson, USA

    Shaojie Tang

Authors
  1. Shaojie Tang
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Correspondence to Shaojie Tang .

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Editors and Affiliations

  1. Computer science and Applications Department, LGIPM, University of Lorraine, Metz Cedex, France

    Hoai An Le Thi

  2. Laboratory of Mathematics, National Institute for Applied Sciences - Rouen, Saint-Etienne-du-Rouvray Cedex, France

    Tao Pham Dinh

  3. Computer science and Applications Department, LGIPM, University of Lorraine, Metz Cedex, France

    Hoai Minh Le

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Tang, S. (2022). Beyond Pointwise Submodularity: Non-monotone Adaptive Submodular Maximization Subject to Knapsack and k-System Constraints. In: Le Thi, H.A., Pham Dinh, T., Le, H.M. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. MCO 2021. Lecture Notes in Networks and Systems, vol 363. Springer, Cham. https://doi.org/10.1007/978-3-030-92666-3_2

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