The research interests of the group of Aichholzer includes discrete and computational geometry, data structures and algorithms, combinatorial properties of geometric and topological graphs, and enumeration algorithms.
On the algorithmic side we are especially interested in combinatorial properties of triangulations and related data structures to obtain efficient algorithms for transforming or counting/enumerating triangulations. This includes consideration of additional restrictions like bounds on the maximum face or vertex degrees.
In the area of discrete geometry we consider typical Erdős-type problems on empty and non-empty convex polygons spanned by (colored and uncolored) point sets in the plane.
On (geometric) graphs the focus lies on the minimum crossing number of complete graphs. Investigating the differences between geometric graphs (vertices are points in the Euclidean plane and edges are segments connecting two points) and general (topological) drawings of graphs has been proven very fruitful in the last few years and will play a central role in my first project part. Moreover, the relation of crossing minimal drawings to combinatorial structures, like k-edges and order types in the geometric case, or rotation systems in the topological setting, are of special interest.
On the teaching side our group covers algorithms, datastructurs, discrete geometry and combinatorial ascpects. Lectures are: Data structures and Algorithms 2, Design and Analysis of Algosithms, Algorithms for Games, Enumerative Combinatoric Algorithms, Discrete and Computatioal Geometry. This is complemented with the usual Seminar and Project courses.