• Covering, Locating, and Detecting Arrays
• Graphs and Hypergraphs
• Supersaturated Designs

The focus of my research concerns application of extremal set theory, graph theory, hypergraph theory, finite groups, and algorithms into combinatorial testing (a pseudo-exhaustive testing approach) and screening designs. The component-based systems have many parameters and interactions of these parameters may cause failures. Covering, locating, and detecting arrays are mathematical objects well-known for their applications in identifying the interactions responsible for these failures. The study of such arrays has been an active field of research over the last few decades. We investigate construction, optimality, applications, and generalizations of these arrays.