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Maximizing profit of multiple adoptions in social networks with a martingale approach

Author

Listed:
  • Bin Liu

    (Ocean University of China)

  • Yuxia Yan

    (Ocean University of China)

  • Qizhi Fang

    (Ocean University of China)

  • Junyu Dong

    (Ocean University of China)

  • Weili Wu

    (University of Texas at Dallas)

  • Huijuan Wang

    (Qingdao University)

Abstract

Information propagation plays an important role in social network, which helps shaping consumer’s purchasing decisions. Most of existing works focus on maximizing the influence of one product. But in our reality life, the majority of the companies produce various products for meeting customer needs. So it is important to learn about how to distribute the limited budget to maximize the companies profits. In this paper, we use the martingale technique to handle the Profit Maximization with Multiple Adoptions ( $$PM^{2}A$$ P M 2 A ) problem, which aims to identify a seed set for each product with overall activation cost at most B such that the expected total profit is maximized. We design a $$PM^{2}AM$$ P M 2 A M algorithm which returns a $$(\frac{1}{2}(1-\frac{1}{e^{2}})-\varepsilon )$$ ( 1 2 ( 1 - 1 e 2 ) - ε ) -approximate solution and runs in $$O\left( (k^{*}+\ell )(m+n)nqp_{max}\ln nq/ (\varepsilon ^{2}\cdot p_{min})\right) $$ O ( k ∗ + ℓ ) ( m + n ) n q p max ln n q / ( ε 2 · p min ) expected time.

Suggested Citation

  • Bin Liu & Yuxia Yan & Qizhi Fang & Junyu Dong & Weili Wu & Huijuan Wang, 2019. "Maximizing profit of multiple adoptions in social networks with a martingale approach," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 1-20, July.
  • Handle: RePEc:spr:jcomop:v:38:y:2019:i:1:d:10.1007_s10878-018-0361-z
    DOI: 10.1007/s10878-018-0361-z
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    References listed on IDEAS

    as
    1. Xin Chen & Qingqin Nong & Yan Feng & Yongchang Cao & Suning Gong & Qizhi Fang & Ker-I Ko, 2017. "Centralized and decentralized rumor blocking problems," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 314-329, July.
    2. Weili Wu & Hongwei Du & Huijuan Wang & Lidong Wu & Zhenhua Duan & Cong Tian, 2018. "On general threshold and general cascade models of social influence," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 209-215, January.
    3. Zhao Zhang & Wen Xu & Weili Wu & Ding-Zhu Du, 2017. "A novel approach for detecting multiple rumor sources in networks with partial observations," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 132-146, January.
    Full references (including those not matched with items on IDEAS)

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