Minimum cost seed set for threshold influence problem under competitive models

  • Ruidong Yan
  • Yuqing Zhu
  • Deying LiEmail author
  • Zilong Ye
Part of the following topical collections:
  1. Special Issue on Social Computing and Big Data Applications


Single source influence propagation based models have been widely studied, but a key challenge remains: How does a company utilize the minimum cost to select a seed set such that its influence spread can reach a desired threshold in competitive environment. One efficient way to overcome this challenge is to design an influence spread function with monotonicity and submodularity, which can provide a nice theoretical analysis of approximation ratio. In this paper, we first propose the Threshold Influence (TI) problem, i.e., selecting a seed set with minimum cost such that the influence spread reaches a given threshold η. Then we present two influence diffusion models named One-To-Many (OTM) and One-To-One (OTO) respectively. On one hand, for One-To-Many model, we prove that the influence spread function is monotone increasing as well as submodular and develop a greedy algorithm with a \((1+\ln (\frac {\eta }{\delta }))\) approximation ratio, where \(\delta >0\). In particular, the approximation ratio is (\(1+\ln (\eta )\)) if \(\eta \) is a positive integer. On the other hand, for One-To-One model, we demonstrate that the influence spread function is non-submodular. Besides, a heuristic framework is developed to solve this problem. Finally, we evaluate our algorithms by simulations on different scale networks. Through experiments, our algorithms outperform comparative methods.


Competitive influence Diffusion model Seed selection Submodularity 



This research was supported in part by the National Natural Science Foundation of China under grant 11671400, 61672524, the Fundamental Research Funds for the Central University, and the Research Funds of Renmin University of China 2015030273, and the Research Funds of Renmin University of China 16XNH116.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of InformationRenmin University of ChinaBeijingChina
  2. 2.Department of Computer ScienceCalifornia State University at Los AngelesLos AngelesUSA

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