Unconstrained submodular maximization with modular costs : Tight approximation and application to profit Maximization

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

12 Scopus Citations
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  • Tianyuan Jin
  • Renchi Yang
  • Jieming Shi
  • Keke Huang
  • Xiaokui Xiao

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Original languageEnglish
Pages (from-to)1756-1768
Journal / PublicationProceedings of the VLDB Endowment
Issue number10
Publication statusPublished - Jun 2021


Title47th International Conference on Very Large Data Bases (VLDB 2021)
LocationTivoli Hotel & Congress Center (in-person and virtual)
Period16 - 20 August 2021


Given a set V, the problem of unconstrained submodular maximization with modular costs (USM-MC) asks for a subset S ⊆ V  that maximizes ƒ(S) − c(S), where ƒ is a non-negative, monotone, and submodular function that gauges the utility of S, and c is a nonnegative and modular function that measures the cost of S. This problem finds applications in numerous practical scenarios, such as profit maximization in viral marketing on social media. 
This paper presents ROI-Greedy, a polynomial time algorithm for USM-MC that returns a solution S satisfying ƒ(S) - c(S) ≥ ƒ(S*) - c(S*) - In ƒ(S*)c(S*) • c(S*) where S is the optimal solution to USM-MC. To our knowledge, ROI-Greedy is the first algorithm that provides such a strong approximation guarantee. In addition, we show that this worst-case guarantee is tight, in the sense that no polynomial time algorithm can ensure ƒ(S) - c(S) ≥ (1 + ε) • ƒ(S*) - c(S*) - In ƒ(S*)c(S*) • c(S*), for any ε > 0. Further, we devise a non-trivial extension of ROI-Greedy to solve the profit maximization problem, where the precise value of ƒ(S) for any set S is unknown and can only be approximated via sampling. Extensive experiments on benchmark datasets demonstrate that ROI-Greedy significantly outperforms competing methods in terms of the tradeoff between efficiency and solution quality.

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