The research of the Combinatorial Optimization Group is centred around combinatorial and discrete optimization problems and graph algorithms. We model, analyse and solve structural and algorithmic optimization and decision problems arising from mathematics, theoretical computer science and natural sciences as well as from applications in industry. We apply a variety of methods from different fields of mathematics, theoretical computer science and economics such as mathematical programming, operations research, combinatorics, complexity theory, combinatorics, algorithm theory and graph theory.
In discrete and combinatorial optimization one aims at selecting an optimal solution from a set of feasible solutions.
The research fields of members of the research group include
Special cases of NP-hard combinatorial optimization problems that can be solved or approximated in polynomial time
Monge properties and related properties
Network flow problems (including parametric flow problems and flows over time)
Assignment problems: linear, quadratic, multidimensional
Analysis of graph algorithms
Industrial applications of combinatorial optimization
Mathematical models in portfolio optimization: theory and applications
The Combinatorial Optimization Group is one of the four research groups of the Institute of Discrete Mathematics at TU Graz. It takes an active part in the Mathematical Doctoral School "Discrete Mathematics" (DK plus programme funded by FWF).