Structural and algorithmic aspects of massive social networks

We study the algorithmic and structural properties of very large, realistic social contact networks. We consider the social network for the city of Portland, Oregon, USA, developed as a part of the TRANSIMS/EpiSims project at the Los Alamos National Laboratory. The most expressive social contact network is a bipartite graph, with two types of nodes: people and locations; edges represent people visiting locations on a typical day. Three types of results are presented. (i) Our empirical results show that many basic characteristics of the dataset are well-modeled by a random graph approach suggested by Fan Chung Graham and Lincoln Lu (the CL-model), with a power-law degree distribution. (ii) We obtain fast approximation algorithms for computing basic structural properties such as clustering coefficients and shortest paths distribution. We also study the dominating set problem for such networks; this problem arose in connection with optimal sensor-placement for disease-detection. We present a fast approximation algorithm for computing near-optimal dominating sets. (iii) Given the close approximations provided by the CL-model to our original dataset and the large data-volume, we investigate fast methods for generating such random graphs. We present methods that can generate such a random network in near-linear time, and show that these variants asymptotically share many key features of the CL-model, and also match the Portland social network.The structural results have been used to study the impact of policy decisions for controlling large-scale epidemics in urban environments.

[1]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[2]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.

[3]  Alan M. Frieze,et al.  Algorithmic theory of random graphs , 1997, Random Struct. Algorithms.

[4]  U. Feige.  A threshold of ln n for approximating set cover , 1998, JACM.

[5]  Madhav V. Marathe,et al.  Formal Language Constrained Path Problems , 1998, SWAT.

[6]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[7]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

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

[9]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[10]  Eli Upfal,et al.  The Web as a graph , 2000, PODS.

[11]  N. Alon,et al.  The Probabilistic Method, Second Edition , 2000 .

[12]  Andrei Z. Broder,et al.  Graph structure in the Web , 2000, Comput. Networks.

[13]  Eli Upfal,et al.  Stochastic models for the Web graph , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[14]  Aravind Srinivasan,et al.  Distributions on level-sets with applications to approximation algorithms , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[15]  Sriram V. Pemmaraju,et al.  Equitable colorings extend Chernoff-Hoeffding bounds , 2001, SODA '01.

[16]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[17]  Stephen Eubank,et al.  Scalable, efficient epidemiological simulation , 2002, SAC '02.

[18]  David L. Craft,et al.  Emergency response to a smallpox attack: The case for mass vaccination , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Walter Willinger,et al.  The origin of power laws in Internet topologies revisited , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[20]  Alan M. Frieze,et al.  A general model of web graphs , 2003, Random Struct. Algorithms.