Abstract: Simple network models often underpin the analysis and synthesis of reliable networks, yet even simple models do not lead to efficient analytic techniques.  As a result, combinatorial techniques have been extensively explored in order to approximate the network structure, or to approximate the reliability measure of interest, with the goal of providing useful analytic tools that can be efficiently calculated.  Here we explore the uses – and also the abuses and misuses – of combinatorial models in practical reliability assessment.  The objective is to understand what combinatorial models can and cannot tell us, to ensure that despite their inherent limitations, we use them when appropriate.

Biography:  Charles Colbourn completed his PhD at the University of Toronto in Canada in 1980; he chaired the Department of Combinatorics and Optimization at the University of Waterloo (Canada), and held an endowed professorship at the University of Vermont, prior to joining Arizona State University.  He is the author of the graduate text “The Combinatorics of Network Reliability”, and has written extensively on techniques for calculating, bounding, and approximating network reliability.  His research interests focus on combinatorial structure and algorithms that exploit it.  He serves on six editorial boards of international journals in these areas.  In addition to research on network reliability in wired networks, his recent research explores protocols in optical, mobile ad hoc, and sensor networks as well as network testing.