The PageRank Problem in Google: A Systems and Control Viewpoint

In this lecture, we study the PageRank problem and illustrate it using the Google search engine as a paradigmatic example. Specifically, we introduce PageRank discussing the so-called random surfer model and the teleportation matrix. Subsequently, we present new distributed randomized algorithms (of Las Vegas type) for its efficient computation. Subsequently, we show the main properties of these algorithms utilizing results of the theory of positive matrices and Markov Chains. Finally, we discuss how these ideas can be extended to different problems of interest to the systems and control community, including ranking of scientific journals, economic complexity, aggregation techniques and consensus of multi-agent systems.