Course : Yπολογιστική Γεωμετρία / Computational Geometry

Graduate course, Spring 2025, Thursday 2 pm, room Γ (Department of Informatics and Telecommunications)  

Intoduction to geometric algorithms and computation. Overview of active research areas of computational geometry. Design and analysis of algorithms, geometric software implementations and real-world applications (such as computational finance and structural biology).

Topics:

- Convexity, convex hulls, volume computation.
- Robust geometric computations, input degeneracy, predicates, filters.
- Voronoi diagram, Delaunay triangulation, alpha-shapes.
- Linear programming algorithms and reverse search, duality.

- Minkowski sum, triangulations and regular subdivisions; connections to algebraic geometry and optimization.

- Randomized geometric algorithms; high-dimensional sampling and volume approximation.
- Geometric data structures, approximate nearest neighbors, spatial databases.