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A Binary Search Double Greedy Algorithm for Non-monotone DR-submodular Maximization

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Algorithmic Aspects in Information and Management (AAIM 2022)

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Abstract

In this paper, we study the non-monotone DR-submodular function maximization over integer lattice. Functions over integer lattice have been defined submodular property that is similar to submodularity of set functions. DR-submodular is a further extended submodular concept for functions over the integer lattice, which captures the diminishing return property. Such functions finds many applications in machine learning, social networks, wireless networks, etc. The techniques for submodular set function maximization can be applied to DR-submodular function maximization, e.g., the double greedy algorithm has a 1/2-approximation ratio, whose running time is O(nB), where n is the size of the ground set, B is the integer bound of a coordinate. In our study, we design a 1/2-approximate binary search double greedy algorithm, and we prove that its time complexity is \(O(n\log B)\), which significantly improves the running time.

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Author information

Authors and Affiliations

  1. Department of Computer Information Systems, Texas A &M University - Central Texas, Killeen, TX, 76549, USA

    Shuyang Gu

  2. School of Computer Science and Technology, Qilu Technology University, Jinan, China

    Chuangen Gao

  3. Department of Computer Science, The University of Texas at Dallas, Dallas, TX, USA

    Weili Wu

Authors
  1. Shuyang Gu
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  2. Chuangen Gao
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  3. Weili Wu
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Corresponding author

Correspondence to Shuyang Gu .

Editor information

Editors and Affiliations

  1. Guangdong University of Technology, Guangzhou, China

    Qiufen Ni

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

    Weili Wu

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Gu, S., Gao, C., Wu, W. (2022). A Binary Search Double Greedy Algorithm for Non-monotone DR-submodular Maximization. In: Ni, Q., Wu, W. (eds) Algorithmic Aspects in Information and Management. AAIM 2022. Lecture Notes in Computer Science, vol 13513. Springer, Cham. https://doi.org/10.1007/978-3-031-16081-3_1

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  • DOI: https://doi.org/10.1007/978-3-031-16081-3_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-16080-6

  • Online ISBN: 978-3-031-16081-3

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