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Stochastic Greedy Algorithm Is Still Good: Maximizing Submodular + Supermodular Functions

  • Sai Ji
  • Dachuan Xu
  • Min Li
  • Yishui WangEmail author
  • Dongmei Zhang
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)

Abstract

In this paper, we consider the problem of maximizing the sum of a submodular and a supermodular (BP) function (both are non-negative) under cardinality constraint and p-system constraint respectively, which arises in many real-world applications such as data science, machine learning and artificial intelligence. Greedy algorithm is widely used to design an approximation algorithm. However, in many applications, evaluating the value of the objective function is expensive. In order to avoid a waste of time and money, we propose a Stochastic-Greedy (SG) algorithm, a Stochastic-Standard-Greedy (SSG) algorithm as well as a Random-Greedy (RG) for the monotone BP maximization problems under cardinality constraint, p-system constraint as well as the non-monotone BP maximization problems under cardinality constraint, respectively. The SSG algorithm also works well on the monotone BP maximization problems under cardinality constraint. Numerical experiments for the monotone BP maximization under cardinality constraint is made for comparing the SG algorithm and the SSG algorithm in the previous works. The results show that the guarantee of the SG algorithm is worse than the SSG algorithm, but the SG algorithm is faster than SSG algorithm, especially for the large-scale instances.

Keywords

BP maximization Stochastic greedy Approximation algorithm 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Sai Ji
    • 1
  • Dachuan Xu
    • 1
  • Min Li
    • 2
  • Yishui Wang
    • 3
    Email author
  • Dongmei Zhang
    • 4
  1. 1.College of Applied Sciences, Beijing University of TechnologyBeijingPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsShandong Normal UniversityJinanPeople’s Republic of China
  3. 3.Shenzhen Institutes of Advanced Technology, Chinese Academy of SciencesShenzhenPeople’s Republic of China
  4. 4.School of Computer Science and TechnologyShandong Jianzhu UniversityJinanPeople’s Republic of China

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