Within the research group "Discrete Optimization" at TUM, we work on combinatorial optimization, discrete mathematics, and operations research. Our focus is on approximation algorithms, linear and integer programming, algorithmic game theory, extended formulations, polyhedral combinatorics, geometric problems, and scheduling.
We construct efficient algorithms for computationally difficult problems and develop the underlying mathematical theory to solve these problems. Applications of our work include chip design, communication networks, health care, logistics, and time-tabling.
Group members
Professors
Scientific Staff & Doctoral Students
Florian Grundbacher
Administrative Staff
Klaudia Bachmeier
Andreas Alpers, Franziska Berger, Andreas Bogner, Steffen Borgwardt, Julia Böttcher, David Bremner, Andreas Brieden, Markus Brill, Christoph Buchheim, Thomas Burger, Lin Chen, Oliver Cooley, Abhi Dattasharma, Katherina von Dichter, Julia Ehrenmüller, Maximilian Fiedler, Elisabeth Finhold, Katherine E. Fitch, Ulf Friedrich, Yiannis Giannakopoulos, Tobias Gerken, Viviana Ghiglione, Simon Gmeiner, Bernardo González Merino, Marinus Gottschau, Felix Happach, Peter Heinig, Raymond Hemmecke, Melanie Herzog, Wei Huang, Alexander Hufnagel, Soubhi Elias Janjal, Klaus Jansen, Markus Jörg, Thomas Kahle, Marcus Kaiser, Günther Kist, Fabian Klemm, Stefan König, Hans-Joachim Kroll, Barbara Langfeld, Marilena Leichter, Silvia Lindner, Jesus De Loera, Katja Lord, Jannik Matuschke, Nicole Megow, Themistoklis Melissourgos, Christoph Metzger, Susanne Nieß, Marc Noy, Nicola Pace, Benedikt Plank, Diogo Poças, Dieter Prangenberg, Wolfgang Riedl, Roman Rischke, Lucia Roth, Stefano Ruggerini, Kevin Schewior, Tina Janne Schmidt, Achill Schürmann, Anastasia Shakhshneyder, Matthias Silbernagl, Kay Sörensen, Tanja Stadler, Paul Stursberg, Anusch Taraz, Thorsten Theobald, Lionel Thorens, Gottfried Tinhofer, Alexandros Tsigonias-Dimitriadis, Sven de Vries, Daniel Vaz, Clara Waldmann, Ekkard Weidner, Markus Wiegelmann, Barbara Wilhelm, Tobias Windisch, Mel Zürcher
Teaching
Among the courses that are closely related to our research are
- Diskrete Strukturen (German),
- Einführung in die Optimierung (German),
- Integer Optimization,
- Combinatorial Optimization,
as well as several special courses such as
- Algorithmic Game Theory,
- Approximation Algorithms, or
- Polyhedral Combinatorics.
Interested in writing a Bachelor's or Master's thesis with us?
We regularly offer theses on different topics in discrete mathematics, combinatorial optimization or discrete and convex geometry. However, please understand that due to high demand, we can only serve students who have taken their last seminar with us and participated in most of the above courses. If this applies to you, you are welcome to send your request to discrete@ma.tum.de.
Optimization Algorithms on Graphs
Are you looking for the shortest route to your destination city? Do you need to assign students to projects based on their preferences? Or are you trying to plan a good school bus route? All of these problems can be modeled and solved through graph theory. The graph algorithms website provided by our research group provides interactive visualizations and explanations for many basic graph theory algorithms.
The "Traveling Salesman" Game
The Traveling Salesman problem asks for a complete round trip through a certain number of cities to obtain the shortest tour possible. While this question can be answered quite easily for just a few cities, it quickly get challenging as the number of cities increases. In the traveling salesman game you can try to beat the computer and also explore the algorithms used to compute optimal solutions.