Research in the chair Discrete Mathematics and Mathematical Programming varies according to projects and interest, buts is mainly centered around four areas:
- Combinatorial Optimization, Approximation & Online Algorithms
- Mathematical Programming & Semi-Infinite Optimization
- Algorithmic Discrete Mathematics & Graph Theory
- Game Theory, Algorithmic Game Theory, Mechanism Design
Within the University of Twente's research structure, the research programs are mainly embedded in the local research institute CTIT (Centre for Telematics and Information Technology). Hence, emphasis is put on the development of mathematical methods and techniques related to logistics and telecommunication. In both areas, algorithmic problems are omnipresent, and these algorithmic problems are investigated from both a theoretical and a computational point of view. That is, we try to understand the theoretical properties of the problem, and we analyze the behavior of algorithms for the problem. From the computational point of view, we study the behavior (or misbehavior) of practical implementations of algorithms, that is, computer programs.
Research in these areas has numerous fields of applications, e.g. process scheduling, production planning, timetabling, healthcare, communication and network design, routing in networks, strategies for pricing network services, to mention only a few. Today's modern technology with its vital concern for the discrete has given Discrete Mathematics new challenges; in particular, since computers require discrete formulations of problems, it has become indispensable to modern computer science. The increasing use of all kinds of networks, especially in transportation and telecommunication, and the further digitalization of our society have led to an eminent role of Mathematical Programming.