Multilevel Algorithms for Tensor and Network Problems

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This proposal develops novel algorithms and software for new classes of large-scale scientific computing problems that are emerging in the areas of tensor-based data processing, Markov chain modeling, and social network analysis. These problems have in common that data sets may be very large ('Big Data'), that new scalable algorithmic approaches are required, and that they have tremendous economical potential in our fast-evolving knowledge-based economy. The proposed research will capitalize on groundbreaking work that was produced recently in the applicant's research group. Tensor-based data processing is rapidly gaining importance in data mining, recommendation systems, and cybersecurity; realistic Markov chain models of complex queueing networks that characterize telecommunications systems (e.g., call centres) are challenging due to the high dimensionality of the models; and advanced social network analysis leads to important competitive advantages for social network companies. New numerical algorithms will be developed for those challenging emerging problem classes. The results of the proposed research promise to be of great benefit to Canada: algorithmic exploration of compute-intensive problems with large data sets is a crucial building block in our rapidly evolving information economy. The numerical algorithms developed in this proposal will have direct applications in Canada's economy and society, for social networking analysis, big data in scientific computing, multi-modal tensor data processing, call centre modeling, and cybersecurity. Moreover, the proposed work will train highly qualified personnel with critical algorithmic and large-scale distributed computing skills that are essential for Canada's knowledge economy.