The design and analysis of advanced algorithms is useful in a variety of applications. Combinatorial analysis of discrete structures is important in analyzing algorithms as well as in understanding the properties of the discrete structures themselves. Established research at UGA in this area has focussed on issues in complexity theory concerning exact (parameterized) and approximation algorithms; exact and asymptotic combinatorial enumeration; structural studies; loop-free algorithms; and graph algorithms. Recent studies have expanded to include randomized combinatorial algorithms, bioinformatics, quantum computation, and algorithms for counting and generating Feynman diagrams.