DGE : Influence Minimization in Networks

The diffusion of undesirable phenomena over social, information and technological networks is a common problem in different domains. Domain experts typically intervene to advise solutions that mitigate the spread in question. However, these solutions are temporary, in that they only tackle the spread of a specific instance over the network, failing to account for the complex modalities of diffusion processes. We propose an optimization formulation for the problem of minimizing the spread of influence in a network by removing some of its edges. We show that the corresponding objective function is supermodular under the linear threshold model, allowing for a greedy approximate solution with provable guarantees. Preliminary experiments on real and synthetic network data show that our method significantly outperforms other common heuristics.

[1]  Michalis Faloutsos,et al.  Gelling, and melting, large graphs by edge manipulation , 2012, CIKM.

[2]  Bernhard Schölkopf,et al.  Uncovering the Temporal Dynamics of Diffusion Networks , 2011, ICML.

[3]  Andreas Krause,et al.  Submodular Function Maximization , 2014, Tractability.

[4]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Ilija Bogunovic Robust Protection of Networks against Cascading Phenomena , 2012 .

[6]  David B. Shmoys,et al.  Maximizing the Spread of Cascades Using Network Design , 2010, UAI.

[7]  Jure Leskovec,et al.  Inferring networks of diffusion and influence , 2010, KDD.

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

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

[10]  Pushmeet Kohli,et al.  Tractability: Practical Approaches to Hard Problems , 2013 .

[11]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[12]  Yifei Yuan,et al.  Scalable Influence Maximization in Social Networks under the Linear Threshold Model , 2010, 2010 IEEE International Conference on Data Mining.

[13]  Jure Leskovec,et al.  Meme-tracking and the dynamics of the news cycle , 2009, KDD.

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

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

[16]  Christos Faloutsos,et al.  Epidemic spreading in real networks: an eigenvalue viewpoint , 2003, 22nd International Symposium on Reliable Distributed Systems, 2003. Proceedings..

[17]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[18]  Le Song,et al.  Scalable Influence Estimation in Continuous-Time Diffusion Networks , 2013, NIPS.

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

[20]  U. Brandes A faster algorithm for betweenness centrality , 2001 .

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

[22]  Masahiro Kimura,et al.  Blocking links to minimize contamination spread in a social network , 2009, TKDD.