TipTop: (Almost) Exact Solutions for Influence Maximization in Billion-Scale Networks

In this paper, we study the cost-aware target viral marketing (CTVM) problem, a generalization of influence maximization. CTVM asks for the most cost-effective users to influence the most relevant users. In contrast to the vast literature, we attempt to offer exact solutions. As the problem is NP-hard, thus, exact solutions are intractable, we propose TipTop, a <inline-formula> <tex-math notation="LaTeX">$(1-\epsilon)$ </tex-math></inline-formula>-optimal solution for arbitrary <inline-formula> <tex-math notation="LaTeX">$\epsilon >0$ </tex-math></inline-formula> that scales to very large networks, such as Twitter. At the heart of TipTop lies an innovative technique that reduces the number of samples as much as possible. This allows us to exactly solve CTVM on a much smaller space of generated samples using integer programming. Furthermore, TipTop lends a tool for researchers to benchmark their solutions against the optimal one in large-scale networks, which is currently not available.

[1]  My T. Thai,et al.  Revisiting of 'Revisiting the Stop-and-Stare Algorithms for Influence Maximization' , 2018, CSoNet.

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

[3]  Edith Cohen,et al.  Sketch-based Influence Maximization and Computation: Scaling up with Guarantees , 2014, CIKM.

[4]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, STOC '84.

[5]  Wei Chen,et al.  Efficient influence maximization in social networks , 2009, KDD.

[6]  Xiang Li,et al.  Why approximate when you can get the exact? Optimal targeted viral marketing at scale , 2017, IEEE INFOCOM 2017 - IEEE Conference on Computer Communications.

[7]  Jure Leskovec,et al.  {SNAP Datasets}: {Stanford} Large Network Dataset Collection , 2014 .

[8]  Hosung Park,et al.  What is Twitter, a social network or a news media? , 2010, WWW '10.

[9]  Rong Zheng,et al.  On Budgeted Influence Maximization in Social Networks , 2012, IEEE Journal on Selected Areas in Communications.

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

[11]  George B. Dantzig,et al.  Solution of a Large-Scale Traveling-Salesman Problem , 1954, Oper. Res..

[12]  My T. Thai,et al.  On the approximability of positive influence dominating set in social networks , 2014, J. Comb. Optim..

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

[14]  Fan Chung Graham,et al.  Concentration Inequalities and Martingale Inequalities: A Survey , 2006, Internet Math..

[15]  Laks V. S. Lakshmanan,et al.  Revisiting the Stop-and-Stare Algorithms for Influence Maximization , 2017, Proc. VLDB Endow..

[16]  Laks V. S. Lakshmanan,et al.  SIMPATH: An Efficient Algorithm for Influence Maximization under the Linear Threshold Model , 2011, 2011 IEEE 11th International Conference on Data Mining.

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

[18]  Alexander Shapiro,et al.  The Sample Average Approximation Method for Stochastic Discrete Optimization , 2002, SIAM J. Optim..

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

[20]  Andreas Krause,et al.  Cost-effective outbreak detection in networks , 2007, KDD '07.

[21]  Jinhui Tang,et al.  Online Topic-Aware Influence Maximization , 2015, Proc. VLDB Endow..

[22]  Nicola Barbieri,et al.  Topic-Aware Social Influence Propagation Models , 2012, ICDM.

[23]  Thang N. Dinh,et al.  Cost-aware Targeted Viral Marketing in billion-scale networks , 2016, IEEE INFOCOM 2016 - The 35th Annual IEEE International Conference on Computer Communications.

[24]  Richard M. Karp,et al.  An optimal algorithm for Monte Carlo estimation , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[25]  Laks V. S. Lakshmanan,et al.  CELF++: optimizing the greedy algorithm for influence maximization in social networks , 2011, WWW.

[26]  Samir Khuller,et al.  The Budgeted Maximum Coverage Problem , 1999, Inf. Process. Lett..

[27]  Shouling Ji,et al.  Minimum-sized influential node set selection for social networks under the independent cascade model , 2014, MobiHoc '14.

[28]  Éva Tardos,et al.  Maximizing the Spread of Influence through a Social Network , 2015, Theory Comput..

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

[30]  David P. Morton,et al.  Assessing solution quality in stochastic programs , 2006, Algorithms for Optimization with Incomplete Information.

[31]  Alexander Shapiro,et al.  Lectures on Stochastic Programming - Modeling and Theory, Second Edition , 2014, MOS-SIAM Series on Optimization.