Introduction to Parameterized Algorithms and Applications

Explore the fourth lecture in a mini-course on parameterized complexity, focusing on methods related to integer linear programming. Delve into advanced techniques for solving structured Integer Linear Programming (ILP) problems using Graver bases. Gain insights into the application of parameterized algorithms in discrete optimization, building upon previously covered topics such as branching, color coding, kernelization, and width-based dynamic programming. Learn about LP-guided branching and kernelization, as well as Lenstra's algorithm for solving integer linear programming in fixed dimensions. This 1-hour and 6-minute lecture, presented by Michal Pilipczuk at the Hausdorff Center for Mathematics, offers a comprehensive look at cutting-edge approaches in parameterized complexity and their practical applications in solving complex optimization problems.