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Influence maximization problem: properties and algorithms

Author

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  • Wenguo Yang

    (University of Chinese Academy of Sciences)

  • Yapu Zhang

    (University of Chinese Academy of Sciences)

  • Ding-Zhu Du

    (University of Texas at Dallas)

Abstract

The influence maximization problem has become one of the fundamental combinatorial optimization problems over the past decade due to its extensive applications in social networks. Although a $$1-1/e$$ 1 - 1 / e approximation ratio is easily obtained using a greedy algorithm for the submodular case, how to solve the non-submodular case and enhance the solution quality deserve further study. In this paper, based on the marginal increments, we devise a non-negative decomposition property for monotone function and a non-increasing decomposition property for monotone submodular function (NDP). According to the exchange improvement (EI), a necessary condition for an optimal solution is also proposed. With the help of NDP and EI condition, an exchange improvement algorithm is proposed to improve further the quality of the solution to the non-submodular influence maximization problem. For the influence maximization, we devise effective methods to compute the influence spread and marginal gain in a successive iteration update manner. These methods make it possible to calculate the influence spread directly and accurately. Next, we design a data-dependent approximation algorithm for a non-submodular topology change problem from a marginal increment perspective.

Suggested Citation

  • Wenguo Yang & Yapu Zhang & Ding-Zhu Du, 2020. "Influence maximization problem: properties and algorithms," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 907-928, November.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:4:d:10.1007_s10878-020-00638-5
    DOI: 10.1007/s10878-020-00638-5
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    References listed on IDEAS

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    1. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions," LIDAM Reprints CORE 341, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Xu Zhu & Jieun Yu & Wonjun Lee & Donghyun Kim & Shan Shan & Ding-Zhu Du, 2010. "New dominating sets in social networks," Journal of Global Optimization, Springer, vol. 48(4), pages 633-642, December.
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    Cited by:

    1. Liman Du & Shengminjie Chen & Suixiang Gao & Wenguo Yang, 2022. "Nonsubmodular constrained profit maximization from increment perspective," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2598-2625, November.

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