Network models of massive datasets

We give a brief overview of the methodology of modeling massive datasets arising in various applications as networks. This approach is often useful for extracting non-trivial information from the datasets by applying standard graph-theoretic techniques. We also point out that graphs representing datasets coming from diverse practical fields have a similar power-law structure, which indicates that the global organization and evolution of massive datasets arising in various spheres of life nowadays follow similar natural principles.

[1]  Mauricio G. C. Resende,et al.  Greedy Randomized Adaptive Search Procedures , 1995, J. Glob. Optim..

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

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

[4]  V. Plerou,et al.  Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series , 1999, cond-mat/9902283.

[5]  Panos M. Pardalos,et al.  Handbook of Massive Data Sets , 2002, Massive Computing.

[6]  Mauricio G. C. Resende,et al.  A Greedy Randomized Adaptive Search Procedure for Maximum Independent Set , 1994, Oper. Res..

[7]  Jeffrey Scott Vitter External memory algorithms , 1998, PODS '98.

[8]  Panos M. Pardalos,et al.  Collaboration Networks in Sports , 2004 .

[9]  Rosario N. Mantegna,et al.  Book Review: An Introduction to Econophysics, Correlations, and Complexity in Finance, N. Rosario, H. Mantegna, and H. E. Stanley, Cambridge University Press, Cambridge, 2000. , 2000 .

[10]  Panos M. Pardalos,et al.  On maximum clique problems in very large graphs , 1999, External Memory Algorithms.

[11]  E. Muñoz-Martínez Small Worlds: The Dynamics of Networks Between Order and Randomness, by Duncan J. Watts, (Princeton Studies in Complexity), Princeton University Press, 1999. $39.50 (hardcover), 262 pp. ISBN: 0-691-00541-9. (Book Reviews) , 2000 .

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

[13]  Leonidas D. Iasemidis,et al.  Quadratic Binary Programming and Dynamical System Approach to Determine the Predictability of Epileptic Seizures , 2001, J. Comb. Optim..

[14]  Olaf Sporns,et al.  Computational Methods for the Analysis of Brain Connectivity , 2002 .

[15]  David S. Johnson,et al.  The Complexity of Near-Optimal Graph Coloring , 1976, J. ACM.

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

[17]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[18]  Panos M. Pardalos,et al.  Supply chain and finance , 2004 .

[19]  Víctor M. Eguíluz,et al.  Scale-free structure of brain functional networks , 2003 .

[20]  D. Watts,et al.  Small Worlds: The Dynamics of Networks between Order and Randomness , 2001 .

[21]  Fan Chung Graham,et al.  A Random Graph Model for Power Law Graphs , 2001, Exp. Math..

[22]  A. Nagurney Innovations in Financial and Economic Networks , 2003 .

[23]  Daniel P. F. Sturdy,et al.  The connectivity of the brain: multi-level quantitative analysis , 1995, Biological Cybernetics.

[24]  Claude Berge,et al.  Graphs and Hypergraphs , 2021, Clustering.

[25]  D. J. Felleman,et al.  Distributed hierarchical processing in the primate cerebral cortex. , 1991, Cerebral cortex.

[26]  Panos M. Pardalos,et al.  NETWORK-BASED TECHNIQUES IN THE ANALYSIS OF THE STOCK MARKET , 2004 .

[27]  Panos M. Pardalos,et al.  Economics, management, and optimization in sports , 2004 .

[28]  P. Pardalos,et al.  Novel Approaches to Hard Discrete Optimization , 2003 .

[29]  J. Håstad Clique is hard to approximate withinn1−ε , 1999 .

[30]  J. Bouchaud,et al.  Noise Dressing of Financial Correlation Matrices , 1998, cond-mat/9810255.

[31]  Albert-Laszlo Barabasi,et al.  Statistical Mechanics of Complex Networks: From the Internet to Cell Biology , 2006 .

[32]  B. Hayes Graph Theory in Practice: Part II , 2000, American Scientist.

[33]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..