Influence maximization problem: properties and algorithms

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 $$1-1/e$$ 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.

[1]  Matthew Richardson,et al.  Mining the network value of customers , 2001, KDD '01.

[2]  Uriel Feige,et al.  Welfare maximization and the supermodular degree , 2013, ITCS '13.

[3]  My T. Thai,et al.  Stop-and-Stare: Optimal Sampling Algorithms for Viral Marketing in Billion-scale Networks , 2016, SIGMOD Conference.

[4]  Enhong Chen,et al.  Activity Maximization by Effective Information Diffusion in Social Networks , 2016, IEEE Transactions on Knowledge and Data Engineering.

[5]  Jon Kleinberg,et al.  Maximizing the spread of influence through a social network , 2003, KDD '03.

[6]  Donghyun Kim,et al.  New dominating sets in social networks , 2010, J. Glob. Optim..

[7]  Xiaokui Xiao,et al.  Influence maximization: near-optimal time complexity meets practical efficiency , 2014, SIGMOD Conference.

[8]  Ding-Zhu Du,et al.  Design and Analysis of Approximation Algorithms , 2011 .

[9]  Xiaokui Xiao,et al.  Influence Maximization in Near-Linear Time: A Martingale Approach , 2015, SIGMOD Conference.

[10]  My T. Thai,et al.  Maximizing the Spread of Positive Influence in Online Social Networks , 2013, 2013 IEEE 33rd International Conference on Distributed Computing Systems.

[11]  D. Du,et al.  Theory of Computational Complexity , 2000 .

[12]  Christian Borgs,et al.  Maximizing Social Influence in Nearly Optimal Time , 2012, SODA.

[13]  Laks V. S. Lakshmanan,et al.  From Competition to Complementarity: Comparative Influence Diffusion and Maximization , 2015, Proc. VLDB Endow..

[14]  Mark S. Granovetter.  Threshold Models of Collective Behavior , 1978, American Journal of Sociology.

[15]  Rajeev Rastogi,et al.  Recommendations to boost content spread in social networks , 2012, WWW.

[16]  D. Du,et al.  Theory of Computational Complexity: Du/Theory , 2000 .

[17]  Jacob Goldenberg,et al.  Talk of the Network: A Complex Systems Look at the Underlying Process of Word-of-Mouth , 2001 .

[18]  M. L. Fisher,et al.  An analysis of approximations for maximizing submodular set functions—I , 1978, Math. Program..

[19]  Wei Chen,et al.  Scalable influence maximization for prevalent viral marketing in large-scale social networks , 2010, KDD.

[20]  G. Nemhauser,et al.  Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms , 1977 .

[21]  Matthew Richardson,et al.  Mining knowledge-sharing sites for viral marketing , 2002, KDD.

[22]  Moran Feldman,et al.  Constrained Monotone Function Maximization and the Supermodular Degree , 2014, APPROX-RANDOM.

[23]  Takuya Akiba,et al.  Fast and Accurate Influence Maximization on Large Networks with Pruned Monte-Carlo Simulations , 2014, AAAI.