Scalable Algorithms in the Age of Big Data and Network Sciences: Characterization, Primitives, and Techniques

In the age of network sciences and machine learning, efficient algorithms are now in higher demand more than ever before. Big Data fundamentally challenges the classical notion of efficient algorithms: Algorithms that used to be considered efficient, according to polynomial-time characterization, may no longer be adequate for solving today»s problems. It is not just desirable, but essential, that efficient algorithms should be scalable. In other words, their complexity should be nearly linear or sub-linear with respect to the problem size. Thus, scalability, not just polynomial-time computability, should be elevated as the central complexity notion for characterizing efficient computation. In this talk, I will highlight a family of fundamental algorithmic techniques for designing provably-good scalable algorithms: (1) scalable primitives and scalable reduction, (2) spectral approximation of graphs and matrices, (3) sparsification by multilevel structures, (4) advanced sampling, (5) local network exploration. For the first, I will focus on the emerging Laplacian Paradigm, that has led to breakthroughs in scalable algorithms for several fundamental problems in network analysis, machine learning, and scientific computing. I will then illustrate these algorithmic techniques with four recent applications: (1) sampling from graphic models, (2) network centrality approximation, (3) social-influence analysis (4) local clustering. Mathematical and algorithmic solution to these problems exemplify the fusion of combinatorial, numerical, and statistical thinking in data and network analysis.