This course will cover a number of advanced topics in optimization and graph algorithms.

Es werden klassische Algorithmen aus verschiedenen Anwendungsbereichen vorgestellt. In die diskrete Wahrscheinlichkeitstheorie wird eingeführt und das Konzept randomisierter Algorithmen an verschiedenen Beispielen vorgestellt.

Advanced design and analysis methods for algorithms and data structures: Random(ized) Search Trees, Point Location, Minimum Cut, Linear Programming, Randomized Algebraic Algorithms (matchings), Probabilistically Checkable Proofs (introduction).

In this course, participants will learn about formal methods for proving mathematical properties of algorithms, including their correctness and running time. The first part of the course introduces Lean 4, an interactive theorem prover, and their foundational principles.The second part applies these tools to the formal analysis of a variety of algorithms.

Students present current or classical results from theoretical computer science.

Presentation of recent publications in theoretical computer science, including results by diploma, masters and doctoral candidates.

This seminar aims to familiarize students with current research topics in fast graph algorithms and optimization.