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Nonsubmodular constrained profit maximization from increment perspective

Author

Listed:
  • Liman Du

    (University of Chinese Academy of Science)

  • Shengminjie Chen

    (University of Chinese Academy of Science)

  • Suixiang Gao

    (University of Chinese Academy of Science)

  • Wenguo Yang

    (University of Chinese Academy of Science)

Abstract

The growing importance of online social networks where people share information with others leads to the emergence of viral marketing, a new way to promote the sales of products. A derivation of classical Influence Maximization (IM) problem is the Profit Maximization (PM) problem that we focus on in this paper. We propose the PM problem with a cardinality constraint in order to make it closer to the real marketing activities. Without a fixed and pre-determined budget for seed selection, the profit spread metric of PM considers the total benefit and cost. The difference between influence spread metric and profit spread metric is that the latter is no longer monotone and lose the property of submodularity in general. Due to the natural form as the difference between two submodular functions, the profit spread metric admits a DS decomposition. What matters is that we design a Marginal increment-based Prune and Search (MPS) algorithm. From the perspective of marginal increment, MPS algorithm can compute profit spread more directly and accurately. Extensive experiments demonstrate the effectiveness and outperformance of our algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:4:d:10.1007_s10878-021-00774-6
    DOI: 10.1007/s10878-021-00774-6
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    References listed on IDEAS

    as
    1. 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.
    2. Xiang Li & H. George Du & Panos M. Pardalos, 2020. "A variation of DS decomposition in set function optimization," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 36-44, July.
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