Algorithms & Complexity

The theory of computation addresses fundamental questions in algorithm design and complexity, including classical problems like shortest path and routing algorithms, and serves as a core area of computer science. Graphs are a universal tool to model data and many real world problems. Our research groups study various aspects of graphs, the theory of computation and more generally algorithms.

Computational Geometry

Many real-world problems have some inherent geometric nature. With the growing demand for efficient algorithms, the field of computational geometry was established in the early 1970s. We study several aspects of the field, including discrete geometry, graph drawings, triangulations, combinatorial properties of geometric and topological graphs. Triangulations have played a major role in science, driving advancements in fields like computer graphics, geographic information systems, and finite element methods.

Distributed Computing

With the rise of distributed systems and large-scale networks, such as the Internet and sensor networks, it makes sense to adapt the theory of computation to explore distributed and decentralized computation. Research in this field focuses on understanding the complexity of these systems, often through classic graph problems, which help model real-world challenges and classify computational difficulty. Two key models, LOCAL and Massively Parallel Computing (MPC), are central to the study of efficient algorithms in distributed settings. The research aims to develop foundational complexity theories for these models and explore the connections between them, with the goal of improving computational efficiency and understanding the limits of decentralized computation.

• Institute of Geometry:
  • Michael Kerber - Topological Data Analysis,
  • Cesar Ceballos - Discrete Geometry and Algebraic Combinatorics,
• Institute of Discrete Mathematics:
  • Mihyun Kang - Combinatorics, Random Structures, and Algorithms,
  • Eranda Dragota-Celi - Problems in P, Combinatorial Optimization, and Robust Optimization,
  • Bettina Klinz - Combinatorial Optimization, Graph Algorithms,
• Institute of Visual Computing:
  • Tom Pock - Discrete and Continuous Optimization,
• Institute of Machine Learning and Neural Computation:
  • Robert Legenstein - Neuromorphic Computing and Machine Learning,
  • Robert Peharz - Probabilistic Machine Learning,
• Instute of Software Engineering and Artifial Intelligence:
  • Johannes P. Wallner - Knowledge representation/reasoning.
     

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