Combinatorial optimization is related to operations research, algorithm theory and computational complexity theory. Combinatorial optimization algorithms solve instances of problems that are believed to be hard in general, by exploring the usually-large solution space of these instances. Combinatorial optimization algorithms achieve this by reducing the effective size of the space, and by exploring the space efficiently.

Members of this CDMTCS research area are also interested in computational techniques for discovering/processing several types of combinatorial objects such as network design (via algebraic and ad-hoc graph constructions) and utilization of bounded pathwidth/treewidth for computing obstruction sets and coping with hard ``real-world'' problems in VLSI design and bioinformatics.