Learn about the modeling and optimization of cascading processes on networks with Professor Pavlo Krokhmal and host Rong Pan, associate professor at the SCIDSE.
Seminar: Modeling and Optimization of Cascading Processes on Networks
Friday, September 21st, 2018
Brickyard Artisan Court (BYAC) 110, Tempe campus [map]
During this seminar, we consider the problem of modeling and optimization of cascading, or “domino”-like processes in networks under the presences of uncertainties. This includes the spread of failures in physical networks, propagation of viruses in computer networks and massive changes in political or consumer preferences in social networks. To this end, we propose a general model that represents a cascading process in a network as a Markov process on a multiscale graph.
We investigate the question of optimal resource allocation that minimizes the time by which the cascading process reaches all the nodes in the network. Under some natural assumptions, we derive analytical solutions for an optimal resource allocation that optimizes the spread of the cascade. These expressions explain the importance of network interactions in the context of the rate the cascade spreads. An optimal resource allocation can be computed in a strongly polynomial time in terms of the size of the network. Importantly, the obtained solution is expressed via a minimum spanning arborescence on an auxiliary graph and provides a hierarchy that classifies the clusters of the network in terms of their importance compared to the cascade propagation.
About the Speaker
Pavlo Krokhmal is a professor in the Systems and Industrial Engineering Department at the University of Arizona. His research interests include decision-making and optimization under uncertainty, stochastic programming, risk-averse optimization and risk management, financial engineering and computational and applied mathematics. He received his doctorate in operations research from the University of Florida in 2003 and a doctorate in mechanics of solids and applied mathematics from Kyiv National Taras Shevchenko University in Ukraine in 1999. He is a recipient of the AFOSR Young Investigator Award and NRC Senior Associateship Award. His research has been supported by the AFOSR, AFRL, DTRA, NSF and private industry. He is Co-Editor-in-Chief of Optimization Letters and an Associate Editor of IISE Transactions and Journal of Global Optimization.